Some other PS2 games worth a look:
The Fatal Frame/Project Zero series (Tecmo): No fighting, just lots of photography.
Glass Rose (Capcom): A PS2-exclusive adventure game, by Another Code/Hotel Dusk producers, Cing. No combat.
Way of the Samurai (Eidos): One of my favorite PS2 games. A significant part of the game is talking to characters, where what you say, and how you say it, can really influence the storyline. The story itself takes place over a three day period, and time passes regardless of your progress. You can choose to get involved in the various events that happen, or keep your distance. There is a healthy chunk of combat involved, though, but most of it is based on balance and stance, rather than confusing button combos. The game was marketed in the west as a beat-em up, but I'm sure whoever bought it expecting such was severely disappointed.
Clock Tower 3 (Capcom): No combat; and quite adventure-like.
Haunting Ground (Capcom): Similar to the above. No combat, as such, but lots of puzzles.
Echo Night - Beyond (Agetec): Sci-fi first-person adventure. A bit slow.
Gregory Horror Show (Capcom): Excellent Japanese adventure game. Definitely recommended.
Under the Skin (Capcom): Your job, as a little alien stranded on earth, is to cause as much panic as you can without being exposed. No combat, per se, although you make use of various zap guns and such. Japanese and underrated.
Personally, I've enjoyed all these games.
