Short of pulling a Flower/Journey style game as we saw in thatgamecompany or coming up with a new genre, I would say that Final Fantasy definitely innovates within it's genre. The problem is that we look at innovation in the same way we used to, which isn't fair. It's like comparing innovation in music these days with the days when rock and roll was born. Back then, when there was practically nothing, there was so much room to show off something new. These days, most major things have already been done.

I think, with the above in mind, Final Fantasy still does manage to do things new far better than any other established series out there that I can think of right now. Of course, I don't play as many games as most.