Cheap ($30+-) and easy to build hot wire foam cutter made from commonly available parts. Cuts styrofoam for surfboards, model plane wings, sculpture, model train or tabletop wargame terrain, 3D sign letters, mold models for lost foam casting, etc.
5/17/2007, Important note! Please be sure to read the comments that other users have left below. There's a LOT of good info there. Check out the links that folks have posted and study what they've said here and you will be able to build a cutter thats suited to your budget and the materials you have access to. There are a lot of alternatives listed or linked below for the frame, the transformer, the wire, the enclosure, and the heat control. Don't underestimate the power of comments! :)
Step 1: Parts
The parts should be pretty easy to find.
1. 12 foot, 16 guage extension cord, about $2 at Home Depot
2. 2 wooden yard sticks from the Home Depot paint department, $.97 each
3. 4 #10-24 x 1.25" machine screws with nuts, $1 at Home Depot
4. 10 #10 washers, $1 at Home Depot
5. About 12 feet of strong, low-stretch string. I used 200 lb dacron kite line.
6. A single-pole dimmer switch. About $10 at Home Depot.
7. A 25 volt, 2 amp transformer, $10.49 from Radio Shack.
8. An electric guitar string, about .10 - .16 size. I think around $1? You can get these individually at a music store or you can use either of the 2 smallest strings from a packaged set. You should keep a spare handy because they can burn out or break from too much tension.
9. A length of two conductor electrical wire with a regular plug on the end. I salvaged mine, but you could use another extention cord if you like.
10. A piece of wooden dowel or stiff plastic rod about one foot long (not shown). I used a bamboo skewer.
11. Optional: 4 regular-thickness CD cases. These are for the box that holds the transformer and dimmer switch, but you would be much better off with something like a "project box" from Radio Shack.