I think Heavy Rain is the biggest innovation, new style game-play and story based gaming/adventure gaming on a console platform is the best thing to come to consoles and I hope it grows.
Motion controls on the Wii are pretty kick-ass though.
I think DLC as an add-on to full price games is actually hindering this generation (This coming from a heavy PC gamer). I find it total BS to have to pay real money for an online map or a piece of clothing for a virtual character.
Online multi-player is nothing new to me (pc gamer side again)
Technological leap: It has made an impact mostly on graphics and the increase of space available has not been utilized to help improve game-play nearly as many games as it should.
Graphics improvements only go so far, game-play should be the what is aimed for more.
Achievements: I could care less about these. It can add replay value a little bit, but that is about it for me.
That sums it up.