I voted 1965 because the Beatles were still working, recording, and (importantly, I think) enjoying themselves as a band. They were exploring new terrain musically and mentally, George was developing his own style, and they were still a hell of a lot of fun to sing along and dance to. This was the funnest year of touring for them (according to Larry Kane), because they weren't freaked out like in 1964 and they weren't burned out like in 1966.
I'm always torn between
Rubber Soul and
Revolver and being my favorite "most representative of the Beatles" album. But in 1965 they did
Help, too. Two great albums in one year: '65 wins!
EDITED TO ADD: And of course Hello Goodbye gets in an eloquent one-line explanation of same while I'm composing my essay. *sigh*