The graphics in Thief were good when it was released, but its blocky models seem particularly odd-looking today. The textures were also fairly low quality (and only 8-bit), but were otherwise very well chosen and implemented. In fact, they've aged pretty well, perhaps almost lending the game more of medieval effect than they did when it was fresh and new--almost like graininess in an old black and white film.
The sound still holds up very well. This game was a pioneer in 4-channel audio, and it holds up very well by today's standards. Sound effects are clear and identifyable with good positional effects, and ambient music (if you could call it that) is eery, subtle and really creates a mood. The only audio problems are that it is sometimes very difficult to determine a sound source's height (maybe not surprising, given 4-channel setups), and audio occlusion is either poor or nonexistent (if there is a partition wall with openings on either side and a guard behind it, his audio will appear to come to you straight through the partition--even if it's solid rock--rather than around it).
Level design is a mixed bag, which I had to knock off a point for. Sadly, this is one of those games where it the phrase "it really picks up after..." must be used. There are some really crappy missions in this game, the first half of the game being a mix of excellent and crappy missions, but after the halfway point, things take a turn for the better and never look back. Actually, I should clarify that the level design itself is all amazing, my least favorite level was admittedly rife with cool architecture...the fun-factor of some of the levels is just lacking.
The story is also one of the best I've ever seen. The cutscenes and mission briefings work with and enhance the atmosphere. The handful of story-advancing cutscenes are so well done, that they may leave an indelible mark on you, similar to how a really well-done movie might. At the very least, they are memorable and incredibly well done.
As of April 2004, this game also holds my designation of having the most satisfying game ending ever. Many FPS games just throw a really hard to beat boss at the end, and you have to scope out the weaknesses and just shoot it until its dead. Obviously, a game like Thief can't do that.