It seems to me that at least one "defining game of a generation" is likely to come at the launch of a console, (SM64, Halo, Wii Sports), but beyond that, they can come out anytime in the generation. Big, new ideas that excite the public aren't necesarily tied to some hardware timeline. In fact, series that debut late in one generation sometimes become defining series of the next generation (Tony Hawk, MGS, Guitar Hero).
And maybe the best example of all is Pokemon. It didn't come out in NA until late 1998, or Europe until late 1999, the same times Game Boy Color was debuting in those regions.
"[Our former customers] are unable to find software which they WANT to play."
"The way to solve this problem lies in how to communicate what kind of games [they CAN play]."
Satoru Iwata, Nintendo President. Only slightly paraphrased.
