Action RPGs are my go to games for this. Some good choices are most of the Kingdom Hearts games and most of the Castlevania games from SOTN onward (including Curse of Darkness and Lament of Innocence). I also like Dissidia and Dissidia Duodecim (012) but I do know that not everyone liked these two games. There are also some more obscure games that might be worth checking out, like The 3rd birthday and Alien Syndrome which are both on the PSP.

“Musou” games (often listed as either ARPGs or beat-em-ups) are also pretty good for this as well. Games like Warriors Orochi and at least most of Dynasty Warriors made after the first (the first game was a fighting game) are good choices. I’m not too familiar with other musou games but I did like Mystic Heroes, which I’ve played the GameCube version of but there is a PS2 version as well.