Indigo Prophecy (or Fahrenheit, outside the US) is one of the weirdest, most interesting games I've ever played. The story starts like a murder mystery and then goes completely off the rails into the supernatural. The QTE sequences are a bit of a pain, but the atmosphere is incredible, and the choices actually matter. It's really aged though – the graphics are rough, the voice acting is dodgy, and it's got some bizarre plot holes. Still kind of a wild ride, but not for everyone!