Personally, I can think of several games for me that fit this description, but I'm a bit low on time, so I'll only mention one for now.
Several years ago (when I was getting ready to go away to college), I was able to purchase my first computer. Sure, my family had had several different computers over the years that I had played games on, but this one was the first that was only mine. It's certainly not very impressive nowadays (Pentium 3 if I remember correctly), but at the time, I thought it was pretty great.
Shortly after getting my new computer, I went out to find some games for it. I didn't have any picked out before I went to the store, I just went to see what I could find. I found one game with a mysterious, cloaked figure holding a bow and arrow on the front of a dark blue box. The description on the back intrigued me, so I ended up getting it. Little did I know a the time how many hours I would spend crouching in corners, listening to doors, putting out torches, and sneaking around trying to steal every last piece of gold and jewelry lying about.
The game I bought was Thief: The Dark Project.
I couldn't get enough of all the sneaking around, so I would usually play every level multiple times before moving on to the next. I liked how the different difficulty levels didn't just mean artificially toughened enemies. Harder difficulties meant that not only did you have to complete all the objectives that you had before, but it added new ones to the list. I liked how most levels had multiple ways to achieve the objectives. I liked all the different equipment and arrow types that were available. I became especially compulsive with dousing just about every torch I could find with water arrows. I liked the stylish cutscenes between levels and the dark story that was being told in them. I loved all the quips that Garrett, the main character, would say as you made your way through the levels. I loved waiting for the perfect moment to club a guard over the head and dragging him into a dark corner so his buddies couldn't find him.
There's just something about Thief that was magic to me. Going back to the game now, it certainly shows its age, but there's still plenty of charm to be found.
