Two and a Half D
Crash Bandicoot (SCEA, 1996) was one of the first games to take two-dimensional platform gameplay and move it into the third dimension. Unlike bidimensional gameplay, which uses sprites for the game world and characters, two and a half D uses three-dimensional character and world models but limits the camera movement in the same manner as a bi-dimensional game: up, down, and in/out on the Z-axis.
When making your two and a half D games, just follow the same rules as with a parallax scrolling camera, with the guidelines of taking control away from the players as listed previously.