Matt and I have a tradition of doing woodworking projects when we're together at our parents' house. We don't have a thickness planer, so we decided to make one based on this YouTube video.
It's a jig for a router that allows it to slide in either direction, but constrains it to a consistent height. The base is made of a melamine shelf and two pieces of 1" aluminum angle. The sled is a piece of plywood with a slot cut in it, some guides to keep it centered on the base, two sides on top to guide the router, and stops on either end to prevent the router from cutting too far.
This thing is easy but tedious to use. You clamp a board to the base, set the height of the router, and run it back and forth over the wood. We limited our cuts to about 1/8" per pass. If you stick with that rule, you'll probably have to do several passes.
We successfully planed pine, oak, and walnut boards from 1" nominal thickness to 3/8" with no problem. The router bit leaves some lines in the wood, but these can easily be sanded away. Other than those lines, the results seemed perfect. The process does take a long time and it isn't pleasant time either, since you're holding a screaming router in your hands the whole time.