I'm a completionist to an extent. Like I've never grinded out the ultimate weapons in any Final Fantasy. "Do you want to grind even more so you can fight more bosses, but with no story, fuzzy?" "Uh, no thanks, FF. Goodbye and thanks for all the fish."
I did search out all of the Riddler's "puzzles" in Batman: Arkham Asylum. However, I have no interest in the challenge maps.
I will grind for stupid crap in FF Tactics though. That's one game I enjoy grinding in.
In Cthulhu Saves the World, I definitely have zero interest in the bonus modes that unlock after beating the game once. No, I don't want to replay the same game with slight variations, thank you very much. The story's so thread bare, there's no motivation to replay the game. But as far as turn based old school JRPG combat goes, it's quite good. Who knows I may replay it one day. I also don't care about the Cthulhu's Angels mode if that story's gonna be just as thread bare and take you to all the same locations as the first playthrough. The humor carried me through the shallow story, but it's not enough to play it again. Amazing deal for 2.69 USD though.
So yeah, a completionist to an extent. If it offers something worthwhile to me, doesn't take too long and is kinda along the way like 16's "The Truth" artifacts in Assassin's Creed 2, then I'll do it. If it's blowing up every single government owned tank in Just Cause 2, then no.
Depends on the game.