it's not uncommon, although in the past the previous gen's version was often a different game than the incumbent gen's version.
i kind of miss the supernes/genesis days where each title was often different. and it was really weird because usually the genesis one had better graphics while the Super NES one had better gameplay other than the jungle book where the Super NES one looked better while the genesis version wasnt impossible.
the genesis version of disney's aladdin (lead by dave perry) looked way better, but the super nes version (by Capcom and lead by Shinji Mikami) not only didnt have an atrocious and very difficult final boss, it had an excellent final boss. i think the genesis one sold better though because of advertising and better graphics but it became obvious 8 years later that shinji mikami was the superior leader.
It was common to see the same titles within one generation, but the OP refers to when you have a game released across two generations of consoles, which did not happen often in the past. For example, Mortal Kombat on the Genesis and SNES, a popular "versus" of two versions of one game of course, but that's within one generation. What the OP means is if you'd then have a new generation of consoles released, say the Genesis 2 for example, and you'd have Mortal Kombat II on that one but MKII would also be released for the first Genesis and the SNES anyway, that's multi-generation and cross-platform too.
A good modern example is... well there's many, let's just take Assassin's Creed IV, it's on the PlayStation 4, but also the PS3 and the 360... but I don't know if the PS4 version has better textures or better LOD or more character polygons count, etc. And come to think of recent games on the 360 and PS3, if there's one of them that I'm surprised didn't end up having a "PS4 version" too is Grand Theft Auto V... or maybe they'll do it when the PC version is completed (or vice versa). So yeah, cross-platforming within one generation is common, but doing that on multi-generations isn't so common.
With this said, however, I have the feeling that since the PS3 and 360 both have something like two or three extra years of life (at least) going for them we'll surely be seeing it happen more often now that the PS4 is here and the One is about a week away. Speaking of which I'm sure that Killer Instinct could be done for the 360 and I'm surprised they haven't made a version for it. But I think only lack of money and development time restrained them, otherwise I'm convinced it'd have happened (the players base is on the 360 for any fighting games, not the XBOX One).