Whether you're a long time fan of Tomb Raider or a newcomer, Anniversary is highly recommendable.
You assume the role of Lara Croft (duh) and plunder all manner of remote locations, all while eluding traps and all sorts of beasties. The controls are taken from the last TR title, Legend, and are very responsive and intuitive. The presentation is very good as well (for a PS2 game) with progressive scan support thrown in.
The other star of the game, besides Lara of course, are the levels. Many of these are very impressive in scale and scope and add to the immersion considerably. Lara's easy to use acrobatics make traversing these areas loads of fun and figuring out the puzzles within is always satisfying.
The combat is solid but not spectacular with a new bullet-time dodge maneuver that enables you to take out enemies much quicker but require some quick reflexes to use effectively. The occasional camera issues can make combat in some stages a bit maddening but can usually be overcome without too much hassle.
Tomb Raider: Anniversary is a shining example of a remake done right. It's budget price make that much more of a must-play. If you like action-adventure games you have no excuse but to play this great game.