From Wikipedia: "Second Sight is an action-adventure video game developed by Free Radical Design and published by Codemasters for Nintendo GameCube, Xbox, PlayStation 2, and Microsoft Windows. It was released on September 21, 2004. The storyline follows MIT parapsychology researcher John Vattic and his attempts to recover his memory as well as the secrets behind his new mental powers."
I really don't know how to explain this game well, so I'll allow Wikipedia to do it for me: "Second Sight emphasizes stealth and minor puzzle-solving over brute force. Vattic uses psionic abilities to supplement his conventional weapons. Being spotted triggers an alarm mode, increasing the number of guards and they search for Vattic. The majority of the psychic powers are meant to be used defensively, avoiding detection or healing wounds."
Here's some random non-stealthy gameplay.
The moon drives people mad.