Through the years, I've played hundreds of awesome games. I usually play games that other players have hated (because I'm a bit weird... lol). Recently, I played Shadows of the Damned, which received harsh reviews from many sites and I don't understand why. The game got some downsides (like picky controls and unskippable cutscenes, which can be annoying when you play through the game twice or more) but the awesome story compensates for those little annoyances.
well one game that i think everyone should play that is a rpg fan is a little known game called Brave story for PSP, i spent well over 80 hours on that game
PSOne: SkullMonkeys! I loved this game back in the day. Great Style and Solid gameplay
PSTwo: Killer 7! Suda51 first big game so you know its got tons of style and a bad **bleep** story
PSTripple: Spelunker HD, great retro style sidescroller game that's a blast to play with friends
PSP: Valkyria Chronicles 2 (& 3) I know the first game on PS3 did alright, but I feel a lot of people missed out on VC2 due to the switch of hardware. I'm still hoping SEGA comes out and brings VC3 to the US on the Vita or something because I'm a huge VC fan.
The idolm@ster 2 is my favorite game, you can check out my post there!