The GTA series is the reason I own a PS2, and i'd go as far as to say GTA3 is this generations Super Mario 64.
Firstly, I don't give a crap about the "mature" themes, they're a tacked on sparkling innovation. Wow, you can beat up hookers, amazing, nobody cares. The game is a unlimited playground of possibilities. It's hard to say why I like the game, it's just a combination of everything in it, mainly the randomness of it all, the fact that I can fly a plane into an old lady, ride a bicycle off a mountain or bungee jump onto the middle of a highway. Then do it again =D
The missions aren't really important to me, I do the missions when i'm bored, rather than the other way around. I enjoy playing around in it, one of the most common things me and my friends do is to take turns seeing how long we can avoid the cops for, with as many stars as possible. Because of the massive variety in the environments and everything, the possible situations are endless, so it never gets old for me. GTA3 / SA have got more play time from me than any other game this generation, it's just pure fun, and it makes me sad it's not on a Nintendo system, it actually feels like a Nintendo game in a way. I believe Miyamoto himself (or another high profile Nintendo developer) admitted he appreciated GTA's open ended gameplay.
Also I think the graphics are fine, there's some amazing looking environments in GTA SA, but some of the glitches balance it out. There's also a few issues with the controls while on foot, but the good outweights the bad by far for me.