That's why I love Nintendo consoles...the best games are usually by Nintendo themselves, and you can't find them anywhere else.
The Xbox and Xbox 360 have so many of their best (or at least most hyped) games on the PC. I've found this to typically be of the Western-developed games, and when Microsoft themselves also have a hand in the PC market (oh, look, Halo 2 is coming to Windows Vista...), it's not like they themselves see them as the same market. Maybe I'm of the minority but I don't mind playing a PC version of a game. All that the Xbox really has IMO is Tecmo, but a few of their games (or gawkfests) aren't enough to make me want to buy an Xbox/Xbox 360.
But it's true that even limited-time exclusives create a sense of what a console has got. Ask anybody and they'll tell you Final Fantasy goes with the PlayStation(s). But think about it...the first six games were originally on Nintendo systems. VII, VIII, and XI are also on the PC (and XI also on the Xbox 360). XII isn't out yet (I don't think). So of the main series FFs, there are currently only TWO true exclusives... IX and X. And though I personally liked IX, most "newschool" FF fans don't really talk about it, so it's really just X in their minds. Even adding XII into the mix, yay, that's just one more game. Sure, PlayStation(s) have spinoffs like FFX-2 and Tactics and various things related to VII, some Chocobo games (which FF fans probably think are too cutesy), and Kingdom Hearts, as well as remakes and rereleases, but there have been just as many or more spinoffs on Nintendo systems (Crystal Chronicles (and its upcoming Wii/DS sequels), Mystic Quest, Adventure, Legend (even if they're part of the Mana and SaGa series), some GBA Chocobo dice game, and everything remade/rereleased on the GBA (and III on the DS). (And now there will be a bunch of mobile phone games.) Point is, Sony =/= Square.
So just because FF VII wowed the world like ten years ago, (and everyone forgot that it came out on the PC later and don't know how to count as it is,) people will always associate FF with the PlayStation (despite there being only two or three true FF games exclusively on them). That probably won't change until someone else gets a new main-series FF game. (FF XI on the Xbox 360 is barely "main-series" and it's not new.)