I know it's already been mentioned, but 999 is seriously a great game. It's a visual novel with point-and-click sequences based around finding your way out of a room. The story is pretty mind-boggling, and it'll take multiple playthroughs to get the whole story. Thankfully the game lets you skip text that you've already read on subsequent playthroughs, so you can just skip straight to the parts you haven't read yet on divergent paths. What escape scenarios you come across change depending on what story path you're on, too.

I really enjoyed it. It sucked my life away until I got all the endings. Wish I had a system that could play the sequel!