Among the big three, what company has come with the most innovations in gaming?

[Veknoid_Outcast]

Nintendo by a mile. The company invented or popularized a number of conventions in the console space: the cross d-pad, analog stick, rumble, motion controls, etc. Plus software like Donkey Kong, Super Mario Bros., Metroid, and The Legend of Zelda were hugely influential and, in some cases, years ahead of their time.