This is a really neat idea.  I have not heard of anyone trying this yet but I don't see why it couldn't be done...  I'm not sure that ABS plastic or PLA plastic are really the best materials for that type of application though.  I have no medical experience so I wouldn't really know but those are really the only materials that a Makerbot can print with at this time.  There are more advanced and more expensive printers that use a different technology called laser sintering that might be a better fit for this application.  I'm no expert though.  I'm just trying to give you more keywords to search for online.  There are some people working on 3d printing human organs for transplants so I don't see why dentures wouldn't work.

ABS plastic or PLA plastic are not hard enough for this purpose.

You could use the water soluble PLA as a lost wax casting material. Lost "wax" casting is a technique where you make a positive of the casting first. A sand or plaster negative mold is then made from the positive. The positive is then melted away. The negative mold us used to cast the part by filling the mold with metal or acrylic resin. The you break the negative mold away from the casting. Teeth and the roof of the mouth are not simple shapes and require complex casting methods to duplicate.

In terms of what materials to make the final product out of commonly dentures are made out of porcelain coated "noble metal". This is what make them expensive. In eastern Europe where people cannot afford dentures they are often made of just porcelain or porcelain coated aluminum.

The complicated bit is the human interface. How would people hold the dentures against their jaws?

Lost wax casting is great for metal parts but requires a kiln.

My grandfather was a dental tech. When I was 10 he taught me how to make dentures. The gum part is made from a very finely powdered pink acrylic when you sprinkle the power into a mould of your teeth, you arrange the teeth that are made of enamel with small metal extrusions to hold them You have you buy or recuperate them. Then you put the liquid hardener on the acrylic with an eye dropper. In an hour or so you can refine it with a dremmel tool or small files for fit and finnish. If you take a mould of your mouth use Geltrate, or bees wax in a mouth shaped tray then you can put fine plaster into the mould. Use a vibrator on it to liquify the plaster and take out bubbles as you put it in. All this stuff is avail able from dental supply stores, and you can even recuperate teeth from old dentures. None of this requires a kiln. We did on the dinning room table. It's more complicated than this, of course, but it's all i can do here. You also have to be aware of "occlusion" Upper and lower teeth touching each other in a bad way. For this you cast upper and lower and align them before you start. Maybe there are dental labs that will do it by mail.

Maybe there are tutorials on line. Good luck.

I am a dental technician. I know for a fact this wont work. Dentures are made out of acrylic with either plastic teeth or porcelain teeth. They are not however made out of "noble metal." The above poster is referring to crowns not dentures. This technology may however work for printing models for the fabrication of crowns and dentures. It may even work for printing the substructures of crowns if the plastic can be cleanly "burnt out" for casting.

Putting plastics into your mouth that can leach toxics is probably not a good idea.  

That said, if the topic is dental uses of 3D printing, there are companies out there.  Some of them are printing wax for use in a longer process:

 http://www.envisiontec.de/index.php?id=80

http://www.toptobottomdental.com/3dprinters.html

http://www.objet.com/INDUSTRIES/Dental/

PLA has been rated for use in food containers by the FDA. I am not that worried though I am sure that using PLA for medical devices requires a different approval.