Diamond, which derives its name from the Greek adamas, meaning "invincible," is famous as being the hardest naturally-occurring substance known, but it also has a number of other interesting characteristics: it is a better conductor of heat at room temperatures than any other material (diamond can conduct 5x as much heat as copper, which is the second most thermally conductive material known); in its pure form it is a good electrical insulator; it is one of the most transparent materials available; and it is extremely strong and non-corrosive.
As diamond is in the same family of elements as silicon and germanium, it can function as a semiconductor and could be used as a substrate for integrated circuits. In fact, in many ways, diamond would be far superior to silicon: it is stronger, it is capable of withstanding high temperatures, and it is relatively immune to the effects of radiation (the bane of components intended for nuclear and space applications). Additionally, due to diamond's high thermal conductivity, each die would act as its own heat sink and would rapidly conduct heat away. It is believed that diamond-based devices could switch up to 50 times faster than silicon and operate at temperatures over 500C.
The problem is that substrates for integrated circuits require the single, large crystalline structures found only in natural diamond. Unfortunately, there are currently no known substrate materials onto which a single-crystal diamond layer will grow, with the exception of single crystal diamond itself (which sort of defeats the point of doing it in the first place). Having said this, many observers believe that a suitable substrate may be developed in the not-so-distant future. When we are able to create consistent, single-crystal diamond films, the semiconductor industry will be revolutionized and (as I discussed in my book Bebop to the Boolean Boogie: An Unconventional Guide to Electronics, ISBN: 0750675438), in addition to being "a girl's best friend," diamonds will also become "an electronic engineer's biggest buddy!"