#5 Valkyria Chronicles
This is the game that effectively validated my purchase of a PS3 back in the day. Up until the release of Valkyria Chronicles there hadn't really been any games on the console that really made me happy to own the console. Valkyria Chronicles changed all that, and still stands as the second best game of the entire console generation for me. One of the main reasons is that this is the only game I have ever played where a specific moment in the story has made me stop playing the game for a while because of how hard it hit. Valkyria Chronicles is a masterpiece in my eyes, and only a few games have ever risen above it.
Hint for my #4:
The best game of the previous console generation. This game's sequel took an earlier spot on my list.