Fullmetal Alchemist Brotherhood fights are my absolute favorite. The anime itself doesn't contain a plethora of them (unlike shows like Bleach) so they grab your attention more. It's cliche, but my favorite fight is the final fight of Ed vs. Father.A very close second has to be the one where Ed starts to fight Scar and Winry gets the gun. It wasn't even that big of a fight, but the struggle Winry had of not killing the man who murdered her parents showed so much of who she was as a person.
Mainly because it wasn't just some big showdown of the main character vs. main villain but everyone was helping (when Hohenheim protecting his sons always gets me) and fighting to protect their loved ones.