As KDR said, its only the crappy games that have this problem. To make a similiar comparison, look at the 1019 memory card for the 'Cube. There's a handful of games that don't support that card (Sonic Adventure 2 being the most famous, though it'll work as long as you don't have 999 blocks..)
Here's a list of some games that 'may not work properly' on PS2:
HereThe one that people might actually care about is Final Fantasy Anthology. I don't think you'll miss the rest.
Here's an expanded list for Model number 75001 (Slimline PStwo?):
Here againAgain, just a couple of major titles, and a bunch of crappy ones.
I guess it goes to show to not dump those 'legacy' systems just yet.