Since I consider the plot an integral part of gaming, and lore an integral part of plot, I would say that the lore is very important to my enjoyment of the series as a whole. It's not constantly on my mind while playing (I'm not running over CHIM when I'm looting a cave in Cyrodiil), but the idea that the world is a lived-in place makes me not just "dungeon delving in a tomb set," but "exploring a tomb."

My game doesn't exist without the lore : P

I do try to set up some story and personality for my character, and I do try to name my characters something that fits in lore. But it's not always on my mind while playing.

Pretty important. I don't always stick to convention when naming a character, but I don't (and won't) run any mods that go against lore. The only mods I will run are to tweak graphics and mechanics a bit.