The types of games I usually play:
Saints Row 2
Oblivion
Morrowind
Fallout 3 (1 and 2 also, so turn based wouldn't be strictly out)
Fallout New Vegas
I've played a couple of Grand Theft Auto games, so not these again.
The Rainbow Six Games
Loved Silent Storm 2 ... until the panzerkleins where introduced to the game. (2004, turn based game if anyone is wondering).
I'd like open world if possible, but missions that allow you to complete them anyway you can would work also. Just not a strictly linear game. I like sword and sorcery games, but feel more in the mood for shoot em up ones at this time.
EDIT: Forgot to mention, this one is actually for the xbox 360.
Thanks