James Tyberius Kirk is the greatest Captain because he is a total badass. There is no subtext to the character and he is all man.
Best movie has to go to the very first. Star Trek: the Motion Picture is my all-time favorite. Kirk is against something he can't fight or fuck, so what does he do? He sits back as another Captain comes along and sacrifices himself and the movie ends with Kirk saying, "Well, we did it."
For all the wrong, and right reasons, I love James T. Kirk. He bangs chicks, he kills what he can't convert and he is all that is man.