Nintendo:
Super Mario
The Legend of Zelda
Metroid
Star Tropics
Luigi's Mansion
PS:
Uncharted
The Last of Us
God of War
Metal Gear Solid
Little Big Planet
Xbox:
Halo
??
These are the franchises I think of as my favorites on the platforms. I've never actually owned an Xbox console, but hope to remedy that someday.
It'll be awhile before I figure out how to do one of these. :P