I haven't built one, but thought this idea was interesting!
Personally, I don't have the fuel stock to make a gasifier economically feasibile....since it looks like you need 3-4lbs/kw...
Stumbled on this guy's homebuilt system. This looks like it would be a good place to start if you're serious.
The little wood stove I posted earlier is a neat little idea, and simple to do..but I think a small nuclear cooker would be more promising. You can't have open flames anywhere I go camping anymore!!
The trick with gassifiers in general is to make sure what you are working with will really gassify - wood is an interesting example. With enough heat, about 1/3 of the wood will turn to gas, add some steam / water, and you can get up to about 1/2 with a really hot fire.
About 50 % of wood is lignin, which is a truly remarkable, 3 dimensional, highly stable material. From a gassifier perspective, it is a PITA, because it just won't. The guy in the link takes advantage of this fact by using his unit to make charcoal, which continues to burn in his little cook unit.
Interestingly, modern paper has very little lignin in it, so it is actually a better source of wood gas than wood itself. There is a fair amount of clay in paper, which will need handling - once again, a little steam helps, but it not a must.