Most of the time, it has to do with smoothing algorithms. Some of these algorithms need 4-edge-polys to achieve predictable and good looking results. Other algorithms need 4-edge-vectors or poles (that is, a vector with 4 edges coming out from it) to get good results.
It also can get better deformations to use 4-edge polys, since the polys are a bit more evenly distrubuted in that case.
I believe that someone in here before said that it has to also do with rendering. However, if you are transfering your models for gaming, you must follow what that program is designed for. Shockwave for example, I think it doesn't matter considering that the program was designed for most 3d modelers use MAX, but that doesn't mean that in some other game engines it is required to use quads. So thats why many of other people say it is good to use quads just so that it is all compatible. Meaning if you're rendering, or transfering it to a game, it will always be compatible using quads.
Also mcWolf is right about when it comes to unwrapping the uv's. The reason why, is that when you do get to uv mapping, you will notice that a great deal of tutorials will say that it is eaiser to apply the Maya's default checker pattern texture to your models. This is so that you can see where the destortions are located. So since the checker board pattern blocks are square, you would also like your uv's to be square. However, this isn't always possible, especially with organic modeling, but the basic idea is you are trying to get as minimal distortion as possible. Trust me it is not fun trying to unwrap a 5 sided polygon.
Furthermore, you also have to keep in mind that there are times that you do want three sided polys such as non-planar faces.