I bought a 40 watt laser cutter/engraver from China via ebay. It cost a little less than $1800. It cuts wood and some thin plastics (acrylic) like this quite well.

Unfortunately, its quality was so terrible, it was little more than a box of parts. I had to build a new stepper driver and run it from MACH3 to get any results out of it. I also had to replace some "greased rail" style bearings with linear ball bearings to get decent accuracy.

The one they've got at MIT probably says "Epilog" on the side and costs somewhere between your car and your house.

Edit: I generally cut "luan" plywood 1/8" or thinner. It seems like about the thickest I can handle. 1/16" veneer gives me the best results.

If you're really into DIY, you can make your own CNC laser cutter http://www.instructables.com/id/Laser-cutter-start-slicing-s...

Otherwise, you're talking $5k and up. However these guys are cheap and fast if you want to farm it out: http://www.pololu.com/catalog/product/749 (I don't work for them, and I'm not an affiliate, just a happy customer)

Take a look at FSLaser (http://fslaser.com). Minimum cost for an entry-level system is $2350+shipping.

Disclaimer: I'm an employee.