I bought a PS2 specifically becuase I've had a PS1 for some time, and a system that plays the old games seemed attractive. I also wanted to be able to continue with the sequels to several of my favorite PS1 games, like Resident Evil (I could have bought a Dreamcast, I guess, for Code: Veronica, but it's looking like the Dreamcast is headed for "dead system" territory), Metal Gear Solid, and Silent Hill. Devil May Cry is another excellent game for the PS2, and I've been enjoying Max Payne (though I'm told it's better on the PC).
I have had no problems with my PS2, though I've read reports that using the vertical holder can "scramble the video card," however that is supposed to happen. The cooling fan is indeed too loud. The RF adapter I purchased to plug the machine into the TV's cable inlet absolutely sucked; the sound was full of static and the picture had interference. I overcame this diffculty by plugging the direct feeds from the PS2 into the corresponding color-coded sound and video jacks in my VCR. (As a result, my VCR must be on for me to see the feed from the PS2.)
The DVD feature of the PS2 is mediocre at best, and the machine comes with no remote. This, too, can be overcome, however; the lovely Mrs. Razor bought me an official Sony PS2 remote. I've been told the early ones had some bugs, but this later version comes complete with IR receiver (which must remain plugged into one of the control jacks -- a disadvantage if you play multiplayer games) and a CD-ROM of software that must be copied to the memory card. The software contains drivers that eliminate some of the PS2's DVD-problems (which include imprecise chapter skipping and a general twitchiness to the menu controls).
So all in all the system has not been perfect, but none of the problems have been catastrophic. I have a DVD player, I can play cool games, I can play my old PS1 games without using the old PS1, and I'm generally pretty happy with it all.