If you can handle 'survivor-horror' style games there are quite a few games with adventure elements on the PS2.
A good example of this is "Fatal Frame 3".
These sell very well and I myself have 24 of them on my PS2 with the final one - Rule of Rose having a very interesting story.
I use a gameshark to make the combat bearable and allow me to concentrate on the story - which is what I get these games for.
