Tomb Raider was developed by Core and published by Eidos on November 15, 1996 for the Playstation, Saturn, and PC. (The European release was approximately concurrent, although Japan didn't get the game until January 24, 1997. published by Victor under the name "Tomb Raiders".) The game, as of this noding, is no longer being published for any platform, but is readily available anywhere used Playstation games are sold, and can be acquired used (or warez/abandonware) for the PC with some effort. The Saturn version isn't particularly rare, but the general difficulty of acquiring Saturn games is an obstacle. If all else fails, there are few differences between this game and the sequels, Tomb Raider 2, 3, the Last Revelation, or Chronicles, all of which can also be acquired quite easily used.
Tomb Raider, for a long while, was the textbook example of the 3-D adventure game, if not the highest quality example. (Not to be confused with graphic adventures or Zelda 64-style 3-D adventures.) The game camera is fixed behind Lara Croft, the protagonist, who can easily be identified by her short-cut brown hair, teal tanktop, short brown jeanshorts, and loose gunbelt. The player moves her about a 3-D environment otherwise much like Prince of Persia, shooting at whatever bats or wolves might get in her way. She progresses through caves and ruins reminiscent of the Indiana Jones series of movies, searching for artifacts. The gameplay wasn't revolutionary, but it was an excellent example of the state of the art in game design at the time, and the game was originally successful for both the quality of the gameplay, as well as Lara Croft's appearance.
While the gameplay of Tomb Raider was no revolution, her appearance, combined with careful promotion, made Lara Croft a popular phenomenon. Core originally designed Lara with as a beautiful woman simply because she would be easier on the eyes; the lead designer was attributed in Next Generation magazine as saying, what with the camera behind the main character for so long, it was "more pleasing to look at a woman's bum than a man's." Of course, with Eidos's successful marketing of the franchise, Lara Croft quickly found herself in the public (and popular) eye, not least because of her appearance. Her popular success, as well as the large piles of money that Tomb Raider earned burst Eidos onto the gaming scene, giving them both the money and the notariety to publish later projects, of which Deus Ex, Daikatana, and Commandos were just a few.
Unfortunately, the later sequels in the Tomb Raider series quickly became excuses to refine Lara's character model at the expense of level design and gameplay, and the series rapidly degenerated, and was all but dead after the release of a mediocre movie starring Angelina Jolie. Hopefully, the latest sequel, Tomb Raider: Angel of Darkness and the new Game Boy Advance outing, Tomb Raider: The Prophecy will redeem the flagging series.
Update: A mediocre movie, a mediocre GBA game, and an overdue, underperforming trainwreck of a game later, the Tomb Raider franchise is flagging at best. The most interesting development is the fact that the creators of Lara Croft and Tomb Raider, Core, will no longer be developing Tomb Raider titles, according to Eidos. Instead, Crystal Dynamics, creators of the Legacy of Kain series, are now in charge of the future of Tomb Raider. Hopefully, they will do a better job of it than Core did.
There are, apparently, a Game Boy Color Tomb Raider and an N-Gage Tomb Raider, the latter possibly based on the movie(?). This node will be updated when I find out more, unless someone else cares to do it first.
Main series
Tomb Raider || Tomb Raider 2 || Tomb Raider 3 || Tomb Raider: The Last Revelation || Tomb Raider Chronicles || Tomb Raider: Angel of Darkness
Portable series
Tomb Raider || Tomb Raider: Curse of the Sword || Tomb Raider: The Prophecy
Sources: GameFAQs, Next Generation magazine, exposure to the series and other awful games