There were a few moments when I did let out a tear or two (and I usually don't cry at movies). Scenes such as Pippin's swearing-in as well as his singing for Denethor (though I'd much rather be swearing at Denethor, the bastard), the haul up Mt. Doom, Elrond stepping aside and no longer interfering in the relationship between his daughter and Aragon, the "You bow to no one." moment, and the last few scenes (the pub, the Grey Havens, and Sam reuniting with his family).
Then again, I can't help but mention the one scene that really moved me in the series. It was the scene in the extended edition (I'm not sure if it was in the theatrical cut) of The Two Towers, when King Theoden tells Gandalf that "No parent should ever have to bury their child." That really hit me hard with Bernard Hill's delivery...that and the fact that my brother spent a good part of this year in Iraq. I'm just glad that he's now home safe and our parents never had to be in that situation.