I actually have two favorite moments from The Two Towers, and I can't decide between them. One is Aragorn returning to Helm's Deep after he's been presumed dead. When he pushes those doors open -- zowie! If I'd been writing this story, that would have been a Moment I looked forward to and wrote toward with great eagerness.
The other moment is also a return to Helm's Deep, but Gandalf's instead. That sunshine floods in, and there he is on Shadowfax, and I'm getting all goosebumpy just remembering it. Beautiful.
As for a favorite line, I dearly love it when Boromir calls Faramir "little brother" in one of the flashbacks in the extended editions This is purely because I absolutely adore it whenever Sean Bean says the phrase "little brother" because of Reasons, and having him use it here was so joy-inducing the first time I saw the extended edition because I'd been hoping and hoping it would happen, but didn't expect it would because why on earth would Peter Jackson know I wanted to hear Sean Bean say that?
(And now I'm starting think that might be in a flashback from ROTK instead. Hmph. I need to refresh my memory, clearly.)