swizzle66: I've also heard people suggest skipping 1, and starting with 2. Is this also a good idea?
I did this semi-accidentally (I won a copy of the second game, but didn't have the first one, so I started with the second game) and I regret it. The first two games share more plot information with each other than they do with the third game. It was still possible to follow what was happening in the second game but I often felt that I was missing background info that would have made things make more sense and have more of an emotional impact.
Then again, I'm somewhat of a purist with these things, so I would always advise playing the games in order. But they do each stand on their own so you could start with later games and then go back and play the earlier ones.
Charon121 is right that the third game doesn't have as many references to the earlier ones, but there are a few books you can find that will summarize what happened before. Also, the third game is the weakest game in my opinion. The plot is good but the engine had some serious limitations, meaning areas are really tiny. This was especially bad in the sections where you can wander the city streets... the city feels really, really small when it should be vast and sprawling. Certain missions from the first two games that take place in small sections of the city are larger than the entire city in Thief 3. Fortunately, the mission level design in Thief 3 does a good job of working with the engine limitations and still providing a good experience.
For what it's worth, I like the second game best, but I'd recommend playing them in order.