Someone jogged my memory regarding the Déagol strangulation scene. When I saw that in the movies, it did seem excessively violent. Possibly because of the realism and the fact that it was one friend killing another, it just seemed to stand out above all the beheading and limb-severing as "a bit too far".
Also, it disturbed me when Sam pulled Sméagol down off the rocks by the elven rope around his neck. In fact, I think I can generalise and say that the good guys get away with some real atrocities which we are somehow meant to forgive them for, or gloss over. In the book, they were the good guys precisely because they shunned these types of actions. For example, Faramir "would not snare even an orc with a falsehood". I believe that the heroes in the LOTR movies should have maintained moral superiority rather than descending into violence.
I found Denethor's running jump in flames in Minas Tirith to be a little gratuitous and unecessary. And Gandalf's line about "thus passes Denethor son of Ecthelion", or whatever it was, suddenly seemed to be inappropriate where it did not so in the book. Most likely because the same sense of horror, tragedy and loss is not present. It almost appears that movie Gandalf is glad to see the end of him! Heroic, indeed.
I can't recall seeing Aragorn decapitating the Mouth of Sauron... is this in the EE? But it certainly sounds horrific. Provoked or not, Aragorn should not have assaulted (let alone killed) an opponent who was not there to fight him, but only to taunt him. If Tolkien had intended Aragorn to be so violent, then surely he would have lopped off Bill Ferny's head as well! And why not Butterbur to boot?