I remember a Dreamcast game called Omikron: The Nomad Soul (which was reviewed on this site years ago). It was a game about ghostly possession that had a few neat ideas surrounded by mediocrity. I guess n-Space was inspired by it because they went to Nintendo with a plan to streamline that concept into a tighter experience. The end result is a GameCube exclusive called Geist which did handle the possession concept better than Omikron but needed more work to become a great game.
Geist revolves around a scientist named Raimi who was investigating a disappearance within a corporate stronghold. After an attack by a monster, Raimi is captured, and his soul is removed from his body. Helped by the ghost of a young girl, Raimi goes on a mission to reclaim his body and take down the corporation. The story is rather weak; I lost interest in the plot very quickly. There are collectibles that reveal more of the story behind the girl who helps Raimi, but I didn't care enough to look for them.
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Fortunately, the gameplay did pick up the slack from the weak story for the most part. Even though the game is first-person with plenty of shooting, the focus is more on exploring and solving puzzles to progress. Though you can move around in ghost form, you can't do much more than recon. The key to the game is possessing a number of people, animals, and even objects. The possessing mechanic is quite amusing and even helps in fights like possessing a crate of explosives to make it blow up an enemy. The possession even comes into play during the boss fights which involve some decent puzzle elements rather than just shooting them. The problem is that people have to be scared into weakness in order to be possessed which got annoying more than once. Another issue is that the level design isn't that good. There are too many paths that lead to nothing and too many places where I got lost. I had to pull up walkthroughs more often than I would've wanted just to get reoriented. Most irritating is that checkpoints are few and far between. I lost a lot of progress several times because I just couldn't get to the next checkpoint. Finally, the multiplayer offerings are an afterthought. Though ghosts do come into play here and there, the three modes are cookie cutter. I lost interest too quickly.
The game looks okay, but I have seen the GameCube do better. The most interesting part is when the view shifts to something else. I giggled a little when I possessed a laptop and saw a guy from the other side of the screen. The sound design is rather good. The sound effects when in ghost form have a cool echo effect which sounds otherworldly, and the music finds the right balance between atmospheric during the exploration and tense during the shoot-outs. Unfortunately, the voice acting is terrible, overacted all to hell.
Geist handled the "possession by a ghost" concept better than Omikron, but the game itself was just okay. Nothing about it was really bad (except the voice acting), but it felt half-baked. It may be worth checking out if you can find it really cheap, but in the end you would probably be better off just watching the movies Poltergeist and The Exorcist again.