If we're gonna count FPAdventure games like Prime, then I have to say, despite the execution being a bit linear..sadly, Geist.
Really, my only real complaints with Geist are its linearity, the controls (GC exclusive), and lack of online multiplayer.
The whole possession aspect was a fun idea, and had a lot of potential, which is why it's a damn shame that the game was so linear with its puzzles, you don't really get to experiment, there's only 1 way to go about doing things. The multiplayer was also really fun, and again the possession gimmick really made it something different. They took the standard deathmatch and managed to give it an interesting twist, host bodies scattered around each with their own weapon, you possess the one you want to use, and can depossess him at any time, but if the body is killed within a certain amount of time after you leave it, it counts as a kill for your opponent. Or the various objects you could posses, from exploding crates you could take control of and wait for someone to cross you and detonate, or the ability to possess a guided missle, or even animals you could use to access secret areas. Then you have things like Host vs Ghost where the ghosts had to possess a human host and try and force them into various death traps, whilst the hosts would fight against the possession and had anti-ghost weaponry designed to kill you. A damn shame it didn't have online.