The Splinter is a concept vehicle currently being built which has most of its components created out of wood. We're talking wheels, frame, suspension, body – pretty much everything but the engine is going to have wood in it somewhere.
When completed, the car will weigh around 1130 kg, and should have a maximum speed of 385kph. Not that you'd want to be driving it that fast – I'm fairly sure that wood doesn't really have the best "crumple zones".
You can follow the car's creation at the student's blog, and check out some of the awesome pictures of both the design and creation of the car at their website. Particularly interesting is their innovative ways to deal with some of the problems associated with building a car out of wood. Like fires. In fact, I'm fairly sure there won't be an ashtray in the dashboard of this car.