It's mostly newer games that don't work at all, mainly as they were designed that way, and look for HDLoader type software when run. At this point I'd say about 98% of all PS2 games work on OPL, and only a fraction of a percent work in HDLoader only still. This thread is a complete mess, but has the closest thing to a up to date and usable compatibility list. I don't think there's any decent compatiblity lists anymore they're either for the now obsolete HDLoader only, or just plain out of date. There seems to be no open source TCP/IP stack for the PS2, so none of the homebrew is smart enough to connect to the internet to get stuff like artwork automatically.

If you are using the internal hard drive you need to make a PARTITION first called 'OPL' on the drive (you have to use ulaunchelf to do this), then stick the art folder and images in there.

Basically you need to make jpg or png images (or just download them from that site), and stick them in a directory called 'ART' in the root of your games device (whether usb or network share, etc). There's a reasonble guide to artwork here.