A feature of video games in which the manner that the player travels is pre-determined on a line, as if on rails. Many arcade shooters have this feature.
The original idea behind this concept is that it allowed a game to feature imagery beyond the technical limitations of the time by using high production value video as a background, combined with limited interactions via traditional graphics for the actual gameplay. A targeting reticle is usually the only thing the player controls in these games.
Later on, games continued to use this concept, even when technical limitations were no longer a deciding factor. This was due to the designers wanting a specific experience for the player to engage in, although it would also be used to make the game easier to develop, since taking freedom of movement away makes the game far less complex and cheaper to produce.
The On-Rails Shooter declined severely, along with the arcades that once housed them (with a few exceptions), but recently a the genre has seen somewhat of a renaissance with ports of First Person Shooters to consoles without either the tech or controls to support a full First Person Shooter. Recent examples include Metal Gear Solid Touch for the iPhone and Dead Space Extraction for the Wii.
The latest trend in marketing On-Rails Shooters is to refer to them as being a "guided experience." While recent On-Rails Shooters are decidedly less simplistic and more immersive than their forefathers, they still have roughly the same style of gameplay. Recent "Guided Experiences" include Dead Space Extraction and House of the Dead: OVERKILL.