After spending a weekend with the debugging unit and a pile of US games, we've been nothing but impressed with the PS2's ability to play PS games. Sure, the games don't look as sharp as they would running on a good PC with a copy of bleem! (that is, if the game you're running happens to be compatible with bleem!, but that's a different story entirely), but the smooth-texture option definitely cleans up the picture, makes games look more colorful, and generally enhances most PS games.
A few games had some graphical glitches here and there. Grind Session, for instance, had a small box around each onscreen sprite - such as your score and other HUD data. Tekken 3's background textures weren't lined up quite right, making them appear to have some small boxes around them as well. Tobal 2 looks great, almost to the point where it would be comparable to some Dreamcast games, but it slows down a bit during the win poses.
Don't forget the fast-loading option, either. With fast loading enabled, games load significantly faster. Most loading bars don't even have time to fill all the way up before the game actually starts. Tony Hawk's Pro Skater's loading bar gets about halfway across the screen before it's completely loaded.
Check out these screenshots of PS games running on the PS2 - we've also got some video available for download.