I've been both surprised and happy over the years about the number of big name first person shooters that have been ported to Linux. It was great to see the original Quake for Linux several years ago, and after that such other games as Quake III and UT2003 made an appearance in penguin land. Now, it's the turn of Doom III to make its Linux debut.
However, given the usual sorts of messes that getting things like this running on Linux can create, its probably the case that you have several questions on your mind about this game and the Linux OS. Which cards will you need to play the game? What graphics quality will certain cards run the game at under Linux? How well does the game play under Linux versus under Windows?
Linuxhardware have the answers in this article here where they discuss all the ins and outs of playing this game under Linux. ATI aficionados will be disappointed to hear that there is only Nvidia hardware support for the game under Linux, and performance in general is... well, you'll have to read the article to find out.