Genre

Rail Shooter: - A game with a first person view point, where the player shoots enemies that pop up from the environment; while the player is automatically moved from spot to spot with boss fights at the end of every level.

More Modern examples

Games in this genre can be found here

Here is a list of notable games to look at:

Virtua Cop

The House of the Dead‎

Panzer Dragoon

Rez

Silent Scope

Sin & Punishment

Star Fox

Time Crisis

Killer7

The Lost World: Jurassic Park (arcade game)

Dead Space: Extraction