Almost all console games for the current generation target 30 fps. A few fast paced games target 60 fps, but never higher than that. 120Hz is mostly for 3D glasses, but honestly the performance on current generation consoles isn't that great with 3D mode. Further to that future consoles are also targeting 30 fps for the most part.
The other consideration is the resolution. Most current gen console games do not render even at 720p resolution, let alone 1080p. In many ways you are actually better off having a lower resolution screen so that the game has to do less work. Its part of the reason I never moved up from my 1366x768 screen, in hindsight its turned out to be much closer in resolution to what the xbox/ps3 actually render at that most of the more modern HD screens.
So no I wouldn't say you would want 120Hz for gaming, with this generation or the next. In practice there isn't a game released for the console that can use it. They barely bother to use 60hz.