I do and I don't. In terms of platforms, it's probably fair to say that I focus primarily on the PS1 and PS2, mainly because I think they both have probably the best selection of games overall. There's a bit of nostalgia attached too, as the PS1 was the system that got me back into gaming after a hiatus in the late 90's, and so I tend to equate the system as offering a very warm, comforting sort of experience, and the PS2 was the first system I ever bought with my own money.
I'm finding I also have a pretty strong fondness for DS and PSP games the past year or so too, as there are a ton of really great games for both systems, many of which can still be found pretty cheap.
In terms of games though, I'm almost exclusively focused on picking up Japanese RPGs, shmups, side-scrollers, and fighting games, both domestic and imported, but it's slow going, since a lot of what I'm after is out of print and rather pricy.