The most recent high-profile entry into the first-person subgenre is Gaspar Noe's "Enter the Void". As first-person movies go, it pays more attention to the little details, like eye-blinks and whatnot, especially in the first scenes of the movie before the main character, uh, dies. From that point, we in the audience get a front-row seat to the guy's soul wandering the Earth. Think of it as first-spirit movie.
"The Lady in the Lake"
Sometimes a filmmaker uses a first-person narrative to tell a particular kind of story or achieve a certain kind of emotional effect. Other times, it's just a gimmick to get curious filmgoers into the theater. "The Lady in the Lake" is decidedly in the latter category, offering viewers the chance to BE detective Philip Marlowe, this time played by Robert Montgomery (in a nice piece of symmetry, the actor whose POV represents the whole movie is also the director of the film). It's not the best Philip Marlowe movie by a long shot, but it is worth seeing for the interesting gimmick alone.
For a first-person noir with a little meat on the gimmick's bones, try "Dark Passage". Sure, only the first third of the movie is done in POV shots, but it's a much more interesting movie than "The Lady in the Lake". The eyes behind the camera belong to Humphrey Bogart as he escapes from prison and hides out from the cops in San Francisco. From there, the territory is well-worn noir, but why would you have a problem with that?
Not all first-person movies simply use point-of-view shots to put you in the main character's head. Some, like "Clean, Shaven", instead provide you with a frontal assault of audio and visuals-appropriate, since the main character of the movie is suffering from schizophrenia. The disorienting effect of strange sounds and abrupt changes in vision give you a rough idea of what it's like to suffer from a serious mental illness, and the identification with the character is almost unparalleled.
The guy holding the camera in the found-footage monster movie "Cloverfield" goes by the name of Hud. HUD stands for "heads-up display", a term for the perspective in first-person video games. Get it? So here we have a first-person movie where we're seeing everything from a camera held by the world's most annoying cinematographer.