Personally, I am a fan of all three.
PC: When I'm playing games here at my PC, I tend to get more into them, for some reason. Playing Morrowind with my lights off at night was one of the best experiences ever, the game is just so beautiful.
Handheld: I like this for games that I quite simply can't put down, simply because if I have a handheld, I don't have to put them downIdeal for Harvest Moon and Chrono Trigger, for me, at least.
Console: I like to be able to play some games online, like Halo, because I can play with my friends. I also like to be able to show off my achievements (though I don't have many yet!), and being able to sit in the living room on the couch with my blanket while I do some heavy-duty gaming all night is always fun <3
Topic: Which is your preferred method of gaming, and why?