Well, the question is in the title. I like Tomb Raider and strategy games (like Civilization 3+4) a lot, and I love the lore/story/immersion that comes with Skyrim/Oblivion/Morrowind.
I am not afraid of zombies and I am not afraid of killing people - but it all depends on the story. Most game stories seem so damn bland. Ideally, I would want to play a hybrid game (RPG, adventure, strategy) with very diverse character classes / unique character development that has a deep story.
Graphics are a plus (I'm not a fan of the WOW color explosion) but not a must.
Which games would you guys recommend?
Vampire the Masquerade: Bloodlines
Fallout: New Vegas
Fallout 3
Dragon Age: Origins + Awakening
Knights of the Old Republic 2
Neverwinter Nights 2
Alpha Protocol
Civilization V
Call of Cthulhu: Dark Corners of the Earth
Amnesia: The Dark Descent
(The last two are adventure games, but among my favorites and lots of fun, especially if you are "not afraid of stuff".)