The Shadow Hearts Series, even though Part 3 is pretty lame in comparison.
The Shin Megami Tensei Games (Nocturne/Lucifer´s Call, Digital Devil Saga 1+2 and Devil Summoner. Partially HARD games)
Even though those games require thinking and are not action games, they should be played by everyone
I´d write more, but I can´t remember what games I have for the PS2...hm.