False teeth?

In the 18th century it was common practise to extract an unhealthy tooth from an individual and replace it with the tooth of a willing and hopefully well paid volunteer.  As unlikely as it sounds, this worked, at least occasionally.  Even now, teeth that have been displaced or knocked out can be eased back into the socket of the jaw (of their original owner, of course) and sometimes heal very well.

You'll be pleased to know however that you need no longer worry (if you ever did) about having a friends tooth forced into your dental arcade. Recent work at the Tokyo University of Science in Japan has shown that a bioengineered mouse molar tooth, grown from embryonic cells and subsequently transplanted into a jaw can successfully 'take root' and restore bone volume in the jaw.  This is the first time a complete organ has been created and transplanted in such a manner.

The transplanted tooth (bottom row) well healed and looking 
good after 45 days.  Note the lack of tooth and surrounding bone tissue in the 
control specimen,which cannot repair or replace itself.
(Image Takashi Tsuji, Tokyo University of Science)

The tooth was grown in a lining around the kidney of an adult mouse, a method which limits its application to humans at this point. However, the signs are good that one day losing teeth and the surrounding supporting tissues may not be such a bad thing - you may be able to get your very own teeth to be grown to order, using your own cells.

It's probably wise not to throw away your dentures just yet however - it's probably going to take a while to perfect the technique for application in humans.

References:
http://www.plosone.org/article/info%3Adoi%2F10.1371%2Fjournal.pone.0021531
http://www.newscientist.com/article/dn20682-artificial-tooth-transplanted-into-mouse.html