I recently went to a video game market and picked up a couple of games for the PS1: Ridge Racer and Colin McRae Rally. I have played Ridge Racer, which seems to be a fun arcade racer with enjoyable physics. I haven't played CMR yet though...
Ridge Racer was one of the very first games I ever bought for Playstation. Also you can load it up and put in your own CD, sometimes getting interesting results!