Well, this is a topic to my liking!
Here you go with the ones I like very much (mostly because of the music):
Genso Suikogaiden 1 & 2
https://www.youtube.com/watch?v=1gbStU9KlV4
https://www.youtube.com/watch?v=kcifUIULqdU
Chrono Cross
https://www.youtube.com/watch?v=923fVDDwaHo
Parasite Eve
https://www.youtube.com/watch?v=M-Tcl6qvfy4
Wild Arms 2
https://www.youtube.com/watch?v=3JfCYgxrQ_M
Breath of Fire 4
https://www.youtube.com/watch?v=OCJ8XHol-D4
Persona 2 PSP (actually, ANY Persona opening will do)
https://www.youtube.com/watch?v=D07mro7NOkA
Jade Coccoon (it's made by Studio Ghibli)
https://www.youtube.com/watch?v=ufsXZXJc_Xs
Threads of Fate/Dewprism
https://www.youtube.com/watch?v=mmA5mBy7m4A
Stella Deus
https://www.youtube.com/watch?v=biQKGFDB_BU
Eclipse Dragon said:
The Wild Arms series traditionally did this until their most recent entry.
Man, I LOVE the Wild Arms games, even the weird one for the PSP. I was so happy to see the first three entries available in the PlayStation Store and re-bought them instantly. Very cool to see I'm not alone with this.