I've never met anyone who considered Khan to be Kirk's nemesis as such... he's always instantly associated with number 2, 'cus he was in it, but original Star Trek in general? I disagree with that. I don't think Kirk has an individual nemesis in that fashion as Batman does.
Perhaps I'm hanging out with the wrong people.
Well he almost had one in Kor from what I hear had they been able to use him more then once like they planned.