Which video game series have left the biggest legacies? How have they?

[Scoobes]

By genre:

Platformer (2D & 3D):

Super Mario Bros.- redefined the 2D genre and popularised console gaming again
Mario 64 - Perfect translation of 2D Mario into the third dimension
Tomb Raider - One of the first 3D platforming games with complex puzzles and mature atmosphere. Franchise has evolved with the times.
Prince of Persia - Original was a 2D masterpiece, but the reboot redefined 3D platforming. Influenced the popular Assassins Creed and Tomb Raider franchises.

FPS:

Wolfenstein - created the genre
Doom - popularised the genre
Half-Life - redefined the single player FPS (e.g. with actual AI and non-combat moments)
Unreal Tournament - showed a purely multiplayer focussed game could sell
Counterstrike - Showed users could create amazing games
Halo - Popularised the genre on consoles

jRPG:

Final Fantasy - Popularised the genre in the West

wRPG:

Elder Scrolls - showed completely free and open world RPGs could sell
Fallout - the first two influenced the genre and the latest games have updated them with a modern take
Deus Ex - demonstrated how combining storyline branching and skill progression of a wRPG with aspects from other genres could work