Quite a few I like. I am more an rpg fan than just shoot em ups. Also I like the old arcade games.
I guess the two series at top of my list are
Final Fantasy (some more than others). Love the cut scenes and music
Resident Evil (really liked 4)
Tomb Raider I chop and change on but still holds a place in my heart for nostalgic reasons. I remember playing the first one on my pc. My goodness the graphics were terrible comparatively.
I have never played Kingdom Hearts as I am not one for cutesie or anime characters. Prefer more realistic. However in Final Fantasy vii I got past that, and it sounds like my kind of thing as I like beautiful graphics and storyline. Will give it a go
Edit: Just remembered another little game I enjoyed, - Vampire:Masquerade Bloodlines.
Now that one was fun hehe.