My vote is with Nintendo. Nintendo is fantastic at controller innovation and they often nail the delivery of it. Nintendo's only problem is that they don't always STICK with it. That is, when the next generation Nintendo system comes all bets are off. But here are a few Nintendo innovations. BTW, to clarify many of these items Nintendo didn't invent, but their integration lead to widespread adoption by competitors (i.e. Sony, Sega, or Microsoft).
D-Pad, Shoulder buttons, four face buttons, analog stick, vibration, wireless controllers with RF communication, microphone integration, headphone jack, touchscreen capabilities, all of these have been widely adopted or adopted by direct competitors after Nintendo. There are also some things that haven't been widely adopted by their competitors at this time, such as split controller setup, NFC, and infrared motion.
Sony has innovated as well. Though it seems "simple", adding extra shoulder buttons and another analog stick was a great thing to do and created the template for most controllers going forward. I also think their resistive trigger idea is very cool. The convenience of having a dedicated share button was also a good idea and one that both MS and Nintendo have copied. However, I wish they wouldn't have removed the select/start buttons.