Edward killing Victoria in Eclipse. This was awesome because Edward never does anything violent (as in kicking someone's ass onscreen) and is usually very kind and controlled. He used his powers to manipulate both villains and then ripped Victoria's head. Pretty awesome.
Seth gets one helping Edward fight Victoria and Riley.
Edward saving Bella from the rapists with his Volvo of Justice.
Alice coming back in Breaking Dawn.
Given Rosalie's usually the Alpha Bitch, her calculating not only the murder of her rapists but how to freak out her ex-fiance as much as possible (saving him for last, wearing a wedding dress) was her crowning moment. Especially when you consider that, from the fiance's perspective, it looked like (the vengeful spirit of) his fiance was coming for him, and he couldn't get away...which is exactly how Rosalie would have felt.
Bella stopping Edward right before he shows himself to the mass and gets killed at the Volturi in New Moon.
In the books Edward reveals to Bella that he had a rebellious stage when he drank human's blood, but he only killed serial killers and rapists, which is awesome already. In the Illustrated guide is revealed that his first victim was Esme's extremely abusive first husband You go Sparkles!
Jacob rebelling against Sam. "I am the grandson of a chief! I wasn't born to follow you, or anyone else!"
Even if it turned out to be all just a vision, the battle sequence at the end of Breaking Dawn: Part II is surprisingly kinda awesome. With major characters dying on both sides horribly, heads and limbs being ripped off, it's as if it's from an entirely different film.
Most notably is a knockout moment where Alice drags Jane directly into Wolf-Sam's awaiting jaws
It's so much more amazing than that. Alice was held back screaming helplessly as Jasper was debilitated by Jane and beheaded. The moment she knows the love of her life is beyond saving, she completelyfuckingsnaps. Jane is her usual smug self at first... and then realizes that Alice is carving her way through the entire sea of Volturi without pausing... and then realizes her power isn't working on Alice and that the adorable pixie psychic isn't stopping... and then takes one glace at the look on Alice's face and runs for her life. She doesn't get far.
Kate and Tanya avenging Irina's death by delivering what is easily the most Family-Unfriendly Death in the entire series to Caius.
Jacob making quick work of the Volturi vampire attempting to attack him from the treetops by jumping up, twisting over in mid-air to bite the vampire's head off, and twisting back over to land on his feet, all without breaking stride while running at full speed with Renesmee straddled safely on his back the whole time.
Aro decapitating Carlisle in the air and Felix and Demetri killing Jasper were pretty impressive.
A lesser one, but Bella's reaction to finding out Jacob imprinted on Renesmee. As mentioned on the main page, she kept her calm about it in the book, only losing her temper when she learns that he nicknamed her daughter "Nessie." Not so in the film: She screams "You imprinted on my daughter?!"
Felix teaching Edward the meaning of a curbstomp battle in the New Moon film, which shows the Volturi as a more effective enemy than shown in the books.
On the subject of the films, every fight scene in Eclipse. With people moving at inhuman speeds, jumping about like they're on the moon, and bodyparts being torn and smashed off frequently, it shows that while Meyer's vampires might sparkle in the sunlight, they can still be Badass.
The climax of Breaking Dawn Part II even if it was all Alice's vision, it shows that the Twilight Vamps are not all pansies and given the opportunity, will prove their worth as a badasses.