He wants to die because it's pretty much the only thing he hasn't done yet.
The show bugs me because he's somehow lived 200+ year, has all of this life experience, and he's still *stupid* about the simplest things. Yeah, we're all stupid about some things when we're 40, but when we're 240? Give me a break.
I predict a serious continuity problem - a la "Heroes" - before very long. They're going to lose track of who he's bumped into over the years. History majors are *not* writing this show, and it's debatable whether or not they're being consulted.
Nonetheless, it's entertaining.