1. Keep the weather out: it provides a continuous barrier between inside and out
   How much it has to keep out the weather depends on climate: in a tropical climate you may only need to keep out the rain, in the desert only the hot or cold, but in most climates you want to keep out both.
2. Hold itself and the contents of the house up
   Each story needs to hold up everything above it, all of the buildings contents and its occupants, and any snow load on the roof.  It also needs to hold up when all the occupants are dancing!
3. Hold itself up under the duress of wind and earthquakes
   Unlike the load due to the weight of things, these forces push the walls over one way or another.

Depending on the building system, each function can be accomplished by separate materials or multiple functions can be accomplished with one material.  Construction is simplified when one material does multiple functions, but the properties of materials (strength, water resistance, heat resistance) often make this difficult or impossible.

Stick frame

This is the most common construction method used in the U.S.  In stick frame construction, the majority of the structural pieces are small and so the building is made up of very many of these small pieces (ie sticks) placed fairly close together which combine to achieve the overall strength.  These pieces are usually wood, but sometimes are steel.  As the pieces get larger and the distance between them greater, it is no longer called stick framing, and instead becomes post and beam system.  Of course, various combinations of the two are also possible.

Stick frame construction is popular because the most common technique, platform framing, allows the use of many standardized pieces of wood and can be done relatively easily and rapidly.  In platform framing, each floor is built separately, one on top of another, and then the roof is added on the top.  The downside of stick framing is that the framing pieces only serve to hold the building up: they don't insulate, keep out rain or resist wind, so other materials must be added to perform those functions.  Typically plywood or a comparable sheet good (like OSB) is used to provide stiffness against wind loads, and some insulating material is filled in-between the 2x4s to give heat resisting, and then entire exterior is covered in a water resistant siding.

(picture: typical stick frame wall and roof section)

Traditionally, stick frame houses were made out of 2x4s, but newer houses are often made with 2x6's instead using a modified framing method often called "advanced framing" or "optimum value engineering", which is an attempt to use less lumber and allow for more insulation.  Taking this concept even further, some houses are built with double 2x4 walls (in various configurations), allowing for even more insulation to be added, but at the cost of using more wood (and labor).

Recently, some builders have been substituting light gauge steel framing for 2x4 in non-load bearing walls.  This can be done using continuing to use wood stick framing for the load bearing parts or going to a post and beam structure. Steel has the advantage of being recyclable (as well as typically having a high recycled content), but comes with the problem of  "cold bridging" because steel is a good conductor of heat.  Steel framers get around this problem by using an exterior layer of foam board insulation or, in the more energy efficient case, using a double wall.

(Adv. framing reference.  Double wall framing options as pictures?)

Post and Beam and Timber Frame

A post and beam structure differs from a standard "stick frame" structure in that rather than using smaller size lumber like 2x4s or 2x6s spaced 16 or 24 inches apart, it uses more sizable lumber like 4x4s and 6x6s or larger spaced 4 feet or more apart.  Structurally, timber framing is a post and beam method, and although traditional timber framing didn't use nails, there is not a significant difference between  the two. The biggest difference in in  implication: in timber framing the large dimensional pieces of lumber are usually left exposed, while a in a post and beam they may or may not be exposed.

Timber frame or post and beam structures are very commonly used in strawbale, cob and light clay buildings.  Timber framing is also combined with SIPs, although this is obviously overkill since building with SIPs generally requires few structural members.

There are various claims out there that timber framing uses less wood than stick framing, but it does not appear that this happens very often in practice.  Likewise, it does not appear that there is any significant difference between post and beam and stick frame construction in terms of wood use.  When the wall in-fill is straw, cob or equivalent, at least the plywood wall sheathing is eliminated--a significant savings in wood.

Although there has been a move away from larger beams (or at least toward engineered wood) in order to reduce pressure to cut old growth forests, this conventional wisdom may be less relevant when applied to FSC certified beams.  By buying larger beams, you're encouraging the woodlot owners to cut some trees on a longer rotation, promoting a forest that is more ecological robust.

Structural Insulated Panels (SIPs)

SIP is short for Structural Insulated Panel, also know as a Stress Skin panel. Physically, an SIP is composed of a sandwich of two layers of a sheathing material (typically OSB) surrounding a foam insulating material (typically polystyrene).  Although each of the component materials is weak on its own, the sandwich is strong because its physical form makes it so that when one skin starts to bend, the other one has to stretch (ie pull apart), and although OSB has little strength against bending, it has a lot of strength against being pulled apart.  Of course a big cut in the skin near any place the panel encounters a bending force will result in complete failure of the panel.  In spite of this, we know of no case of SIP failure.

Environmentally,SIPs are touted as saving wood as compared to stick framing, and although that is clearly possible, it seems to depend on whose SIP system you use and the particular details of the structure.  At the moment we have no good data on this.  Even if there are wood savings, many debate the environmental benefits of the component materials: OSB and polystyrene board (see materials for more info).  These issues could turn in favor of SIPs if there was a good source of FSC certified (or equivalent) OSB and the use of recycled content polystyrene.  Although these are valid points, the alternative systems have their own drawbacks, and there is no strong argument for any system.  One advantage of foam board insulation is that it is very air tight and has a high R-value per inch of material, so a 12" SIP will likely perform better than any comparable 12" construction system.

The cost of SIP framing appears to be comparable to stick framing: the materials are much more expensive, but there is significantly less labor involved.  A number of sources have reported cost savings using SIPs, but all seem to agree that the savings only comes with experience.  To get significant cost and materials savings may mean designing the shape of the house with SIPs in mind, so custom buildings may not see much savings from using SIPs.

ICFs

Insulated concrete forms are hollow, block like structures that stack together like bricks and are then filled with concrete.  These forms are then left in place to function as insulation for the wall, resulting in a wall that is better insulating while also using less concrete than a standard poured concrete wall (the implication is that typical walls use more concrete than necessary, since the ICF add little strength, but I've never seen this topic discussed.)  Most ICFs are composed of virgin polystyrene, but at least one product (Rastra) uses recycled polystyrene. There is also at least two products (Faswall  and Durisol) that use wood chips instead of polystyrene.  Since concrete has little insulating value, the insulating value of the finished wall is due to the ICF itself.  A typical wall is at least 50% concrete, so the R-value of the wall is much less than other system which consist of a higher percentage of insulation for the equivalent thickness.

Although it is possible to use ICFs for all a buildings walls, it generally only makes sense to use them below ground in the case where the space needs to be insulated since no other wall system works below ground.  Exceptions to this would be areas that have an exceptionally high wind load, and areas where wood is not generally available, or someone who just wanted to avoid using wood.   The typical use of ICFs would be in heated basements and daylight basements.

ICFs are often considers a "green" building material, but since both concrete and polystyrene come with a significant environmental burden, this is not an easy argument to make, other than as a direct replacement for solid concrete walls.

ICFs have a fairly high amount of thermal mass, but because both sides of the wall are insulated, the thermal mass isn't well exposed to the interior, limiting its ability as a temporary heat storage material. 

Strawbale

Building with straw bales is not a new idea, but was essentially not practiced at all until it had a revival in the 1970s.  Straw bales are produced by the same baling machine that makes hay bales, but contain only the stalk of the grass, not the nutritious top part of the plant, and are typically produced after the grain (or hay) has already been harvested.  Straw is considered a waste material, although this may be more due to the fertilizer intensive industrial style of agriculture than an inherent property as many organic farmers will till crop residue back into the soil to restore nutrients and maintain the "airy" nature of the soil.  Even if straw isn't really a waste product, it seems likely that some of it (possibly even a large percentage of it) could be harvested as bales by using other waste organic material to enhance the soil.  (note: since I've yet to find an organic farmer to ask, I don't know how much of a big deal this is).

Strawbale buildings come in two basic varieties: load bearing, in which the bales hole up the roof, and non-load bearing, in which a post-and-beam structure holds up the roof.   In either case, the bales are stacked like bricks,   and then finished inside and out with a plaster of some sort, either a cement stucco, a lime plaster stucco or an earthen plaster.  For load bearing structures, the bales are heavily compressed before applying the stucco.  In spite of this compression, over time the roof load tends to transfer to the rigid stucco.  In both system the lateral loading (sideways, typically shaking force applied to the walls by wind gusts or earthquakes is also taken by the stucco.  Since the stucco is brittle, any force applied to the wall that is large enough to cause movement (beyond the small amount the stucco can tolerate) will result in cracks in the stucco, greatly reducing its strength.  Because of this, in areas with significant lateral (sideways) loading,  it is common to build only non-load bearing structures.

Since bales come in two sizes: "two string" and "three string".  The actual dimension varies somewhat depending on the baler used.  Two string bales are generally 18 thick, 14-16" high, and 32-39"  long.  Three string bales are 24" thick, 16" high, and 42-48" long.  Because these create very thick walls, the designer must be aware of the space they take up in placement of windows and doors, especially near inside corners.  Complex exterior shapes can be very problematic, and so straw bale buildings tend to be simple.  When small bump-outs or large areas of glass are desired, that part is often done as stick-frame.  Although it is possible to modify a bale before using it, doing so is tedious and results in a much less compressed bale, so designers will usually try to lay out the floor plan to allow for as many whole bales to be used as possible.  This could involve either making the dimension of the house be divisible into whole bales, or in the case of non-load bearing structures, making the posts on four foot centers so bales fit between them.

Bale homes have very deep window sills.  In most climates it is best to locate windows to the outside of the bale so as to minimize any exterior sill where water might collect.  Doors can be located on either surface, since there is only ground under the door sill.  Both window and door liners can be either perpendicular to the window (which is the easiest to build), or can be at an angle which will allow more light to come in.

A significant issue for strawbale is keeping the bales dry, both during construction and for the life of the structure.  Although wood is also susceptible to rot, straw has a much greater surface area exposed to the air, and hence will rot dramatically faster than wood.  Because of this low tolerance for moisture, bale wall are usually built to be much more permeable than stick frame walls.  This generally means that large overhangs much be used to keep rain off the structure, as stucco is fairly absorbent.   These overhangs may reduce both the potential for solar gain, and the ability to amount of light that comes in the windows.  Many of the recent straw bale buildings are in hot dry climates where these limitations aren't a problem.

Bale walls were once advertised as having an R-value of 50, but the currently accepted figure is more like 30, which is the equivalent to about an 8-9" insulated stick frame wall.  Non-load bearing bale structures are typically a wood post and beam, but steel is also used.  The posts can either be solid wood, or constructed box columns made of smaller dimensioned wood (2x4s or 2x6s) on two sides and plywood on the other two.   Because the inside of a bale wall is plastered, there is a significant amount of added thermal mass-- typically less than would be needed for a fully passive solar house, but still a sizeable contribution (how much? look this up...)

At the present time (2007), there is not one, or even two standard ways to build with bales even if you restrict yourself to the more common non-load bearing variety.  There are different kinds of posts that are used, and different ways to integrate those posts in with the bales.  As time goes on, its is likely that some kind of standard will evolve, at least regionally: until then don't expect to look up how to build with bales and find one way to do it.

The conventional wisdom is that it is possible to build a bale house quite cheaply, and unfortunately this isn't the case.  The exterior skin of the house typically only accounts for 15% of the total cost of the house, so unless you're planning on doing most everything yourself and keeping the quantity of finish details to a minimum, you'll find that bale houses usually cost the same as standard construction.

Adobe/Cob

Both adobe and cob are mixtures of sand, clay and straw, which when dry forms a wall that is not unlike concrete--not nearly as strong, but less heat conductive.  Still, compared to an insulated wood framed house, neither of these materials is a very good insulator.  The lure of these materials is that they are readily available, non-toxic and decompose easily. Unfortunately that also means that great care must be taken to protect the walls, lest they decompose before the desirable lifetime is over.

Adobe is typically constructed in blocks, dried in the sun, creating a home that is usually fairly conventional looking, while cob is generally applied by hand until the wall is tall enough, often built into whimsical curving structures.  In each case, sand provides compressive strength, straw provides the "breaking" strength, and clay (possibly with some Portland cement added) acts as the glue to hold the whole mess together.

ecause of their low insulation value, both of these building methods should have added insulation somewhere.  If the insulation is on the outside, both of these wall systems will create a large amount of thermal mass in the house--not necessarily in the best possible place for it, but presumably still acceptable (find out more about this...)

Papercrete etc

Papercrete is just adobe/cob that uses recycled paper in place of the straw.  Unlike cob or adobe, papercrete builders are trying to use a high quantity of paper so that the walls have a high insulation value. The limitation here is that as the quantity of sand and cement go down the resulting material grows weaker.  It seems likely that it is not possible to build a wall with papercrete, that is both structurally strong and highly insulating (although its certainly easier if you don't have to deal with earthquakes, hurricanes and large snow loads).

Rammed Earth

Rammed earth is even more like concrete than adobe or cob, in that is is mixture of clay, sand, gravel and often either lime or Portland cement added for strength. Because of the poor insulating value of the resulting wall, the only practical rammed earth wall system requires it to be some kind of sandwich around an insulating material (polystyrene is the obvious choice, since rammed earth absorbs water).

Like adobe & cob, rammed earth has a very large thermal mass.  An un-insulated rammed earth structure will perform quite well in any climate the is sunny almost every day because it will absorb heat from the sun, raising its effective R-value dramatically. In the lack of the sun's radiant energy, the wall will tend to settle at the average daily temperature and stay there...presenting a constantly cold surface during cold weather.   The downside to having a large amount of thermal mass is that you can't easily change the temperature even if you want to: once the house gets too cold or too hot it tends to stay that way for a couple of days.

Final thoughts

Each of these building techniques has its own user groups and cheerleaders, and each group will claim their building technique is better than everyone else's.  Needless to say, they're all wrong, because each has its own unique set of tradeoffs. In considering each of the techniques, you need to not only evaluate their relative merit, but to figure out whether you can find the materials and expertise to build in that style.  If you live in an areas with building code, you may also find the building department not especially open to alternative construction techniques they are not familiar with.  Although not insurmountable (patience and charm help), it can add a significant burden to the construction process.

Resources

Building with Vision: optimizing and finding alternative to wood, Watershed Media (2001).

Buildings of Earth and Straw,  Bruce King covers all the structural issues of these alternative buildings.

Wikipedia article on strawbale at: http://en.wikibooks.org/wiki/Straw_Bale_Construction 

SIP manufactures association at www.sips.org

Insulating Concrete forms association at www.forms.org

Wikipedia article on rammed earth http://en.wikipedia.org/wiki/Rammed_earth