The best fights always seem to revolve around Ichigo vs. powerful character. Just about every single fight he has had was amazing (after he hit the Soul Society that is, everything else was okay action).
Ichigo vs. Ikkaku
Ichigo vs. Renji
Ichigo vs. Kenpachi (awesome fight)
Ichigo vs. Byakuya (mini-fight) then Ichigo vs. Byakuya (full fight, AMAZING)
Ichigo vs. Grimmjow (1, 2 and 3...3rd was THE SHIT)
Ichigo vs. Ulquoirra (first fight was so-so, final battle was EPIC)
Ichigo vs. Gin Ichimaru (while he was on the losing side, I mean he was fighting Gin...AWESOME).
And I'm sure whenever he fights Aizen, we'll get more awesomeness.
Aside from Ichigo's fights, there are plenty of other amazing battles...I mean come on, the series IS about the battles afterall (if it wasn't, we'd be reading/watching Death Note, amirite?).
Uryu vs. Mayuri
Kenpachi vs. Tosen
Every single Espada fight
Aizen vs. just about everyone except those in Huenco Mundo.