I'm going to throw in another vote for Mark of the Ninja. It's impeccably well done, with clear indications of how much noise you're making, or how visible you are. Not once did I mess up and feel like it was because of some sort of ambiguity or lack of feedback from the game.
Deus Ex: Human Revolution also has good stealth, if you choose to play it that way. The camera goes into a 3rd-person perspective when in cover, if you find the 1st-person viewpoint to be too claustrophobic for stealth.
I'd recommend any of the Metal Gear Solid games, although 1 and 2 are a bit dated, with their fixed-position cameras.
Lastly, I recommend that you try to grow accustomed to Thief. I first played it myself last year, and I also found its datedness to be off-putting. However, after sticking with it, it sucked me right in. It feels extremely satisfying to pull off a heist without really having any sort of supernatural powers, like what you'll find in a lot of modern stealth games (not saying that's necessarily a bad thing). For the most part, you're relying on your wits, and it definitely feels empowering.