Team 95 has used plywood chassis numerous times in the past. Some pictures:
http://www.frcteam95.org/wp/picasa2/...aszetaArchives
http://www.frcteam95.org/wp/picasa2/?album=Archives
Very simple implementation: plywood sheets cut to size usually with a combination of table, circular, and jig saws, and then bolted together with 1x1x0.125 angle aluminum and 1/4-20 bolts. Countersunk bolt heads on outside surfaces of the robot.
Probably not the lightest assembly method ever, but every robot built this way survived quite nicely in the days before bumpers. It is also very cheap and easy to assemble and build with only basic hand tools (circular saw, jig saw, and a drill will get you there) and doesn't require a ton of precision to work well.
9-layer baltic birch is what we've used in basically every instance. Easily available at Home Depot and other hardware stores, very strong, and comes with a good finish.