I'm on my second PS2, but there was nothing wrong with my first one. I just wanted an NTSC machine instead. I've not had any trouble with either of them - but my X-Box appears to be falling apart, because it gets harder to play on a weekly basis.
I do know some people who've had trouble with their PS2s, like my girlfriend, but that's probably more because her moron stepdad tried to fix it himself instead of sending it off anywhere for, you know, fixing and the like.