I love this game, been playing it recently. Great release. 4, perhaps 4.5 out of 5.
I played Thief 1 LOOONG ago and didn't beat it, don't recall much of a story either, just went mission after mission.

Now I played Thief 3, and although there are mentions to Garrett's past, I didn't feel like I was missing much. It's a great standalone game as far as I could see (didn't beat this one either though).

It did suffer quite a bit from being developed parallel for consoles, rather than PC first ans ported after (same with Deus Ex: Invisible War,) but still a worthy game. I hope Thi4f is waaaaaay better!

I liked the story in Thief 1 the best. The entire theme of it was the clash of magic versus technology. The missions involving Constantine were where the plot really begins. The final big explanation of what was going on (and why the title of the game is "The Dark Project") is in a journal you find in one of the last missions, which I think is required to progress, though if it's not, then it might be possible to miss a major revelation. The end of the game leads directly into Thief 2.

I love that game. I've watched just the cinematic videos from time to time to remind me of the exciting, interesting story. Also, the scope was large. There were no levels in Thief 3 that were as big as the cavernous Bonehoard, a huge underground crypt full of zombies.

Thief 2 is bigger, and more varied in types of missions. The story is big, and also interesting. The templar faction has had a split, with a charismatic leader leaving the Hammerites and forming the Mechanists, delving into technology the Hammerites considered too dangerous. He's a madman, and it can be horrific to find out what he's doing and planning.

An unexpected ally returns from the first game, and in this game, the cinematics introduce certain characters that will play a big part in the third game, in the Keeper faction. It also has very large levels, like the roof-running mission.

There are also hundreds or thousands of fan-made missions for the first two games. Mainly for the second, since it was an improved engine.

The third game has a wide mix of mission types, and better graphics. The atmosphere, however, I found to be much less tense, because it turned out to be too easy to escape from guards if they spotted me, while in the first two games, it was very tense and challenging. It was also very easy to kill guards, whereas in the first two, combat was something to be avoided. I also thought the use of rope/vine arrows to get to higher places from the first games was more fun than the climbing gloves from the third. The pagans were also much more interesting in the first games. Overall it was a fun game to play, though, and had an atmosphere of its own, though different.

The third game might be a good introductory game for new players who might be put off by the poor graphics of the originals, except that they'd miss out on how it fits in the story. The ending was a very nice touch -- a full circle ending that recalled events in the first game, and showed a long-resisted change in Garrett's character. I think the player would benefit from having played the previous ones.

EVERYone would benefit from having played the previous ones. =]

This! I could not say it better.:)