Ultimately, it's going to take developers alot of guts to break the genre barriers. There are, however a few games out there that might end up breaking the genre.
Alan Wake would be a great example. Yes, there's gunplay, but the main focal point is to tell a story and incorporate some great horror/adventure elements into it.
Ultimately, you could EASILY do a great FPS game that was non-violent and neat using UE3 or Oblivion's engine. I always thought maybe doing a mystery game using Radiant AI (Oblivion's AI engine), and an Oblivion-type world, but modern for maybe a mystery who-done-it sort of game would be interesting. Ultimately, you could use Wii or standard controls to do alot of things with games anymore. The horsepower is there on 360/PS3 to have some ultra-impressive (both visually and gameplay wise) for all kinds of great cenematic elements.
With all the advances in AI, lighting, improvements to dialogue, disk space, and such, we could see some great adventure games out there that use the greatness of the 3 next-gen systems to make some really fun games. One day, hopefully a few devs end up doing more games like Alan Wake, Banjo Kazooie, and such.
Ultimately, there will be a compromise of the M-rated games and the E-rated games. I think Crackdown without the violence would be a good seller - half of the game was a better-than-Mario platformer because of the sheer amount of things you could do. Heck, the reason I love GTA isn't the violence, but the open-ended gameplay and huge world to explore, ala Oblivion. I feel that many gamers probably buy games like those not to merely just kill people, and save the princess, but to explore a large world to excape to. One day, hopefully devs wake up and realize the storytelling medium of video games lags far behind AI and every other element of the video game experience.