Edward is telling Bella what's on the minds of people at a restaurant:
"Money... Sex... Money... Sex... Cat."
Ironically, Edward was quite distressed at that point in time. Narm or mild Tear Jerker, take your pick.
New Moon
Alice (to Edward, about Bella): I think she's having hysterics. Maybe you should slap her.
Bella tells Edward she is just too young to get married.
Edward: Well, I'm nearly a hundred and ten. It's time I settled down.
Eclipse
Emmett: Fall down again, Bella? Bella: No, Emmett. I punched a werewolf in the face.
Alice and Edward play chess, and because one is a mind reader and the other can see his future actions, the game is played almost entirely in their heads and is over by the second move.
Edward: You know, Jacob, if we weren't natural enemies and also you weren't trying to steal away the reason for my existence, I might like you. Jacob: Maybe, if you weren't a disgusting vampire planning to suck the life out of the girl I love... well, not even then.
Bella: You won't sleep with me until we're married? Edward: Technically I can't ever sleep with you. Bella: Very mature, Edward.
This whole conversation:
Charlie: You are being... careful? Bella: (horror)
Jasper: Rule number one... never turn your back on your enemy.
Breaking Dawn
Alice: I'll play you for it. Rock, paper, scissors. Edward: Why don't you just tell me who wins? Alice: I do. Excellent.
Rosalie making a doggie dish out of a steel bowl for Jacob. Even Jacob concedes writing "Fido" on the side was pretty funny— before bouncing it off her head!
Film series
Twilight
Charlie tells Bella to bring Edward in as he cocks a shotgun.
"...I had an adrenaline rush. It's very common. You can Google it."
Jacob: (deadpan voice) I kissed Bella ... and she broke her hand ... punching my face.
And when Bella's getting her hand fixed up:
Emmett: What, did you try to walk and chew gum at the same time again, Bella?
Bella: I punched a werewolf in the face.
Emmett: Bad-ass.
Bella says Edward is 'old school'. Charlie asks her if it's code. Bella is then royally grossed out.
The somewhat meta awesome of:
Edward: Doesn't he own a shirt?
Breaking Dawn
The speeches given by Emmett, Jessica, Charlie and Renee at Edward & Bella's wedding reception.
Seth 90% of the time. Mixes this with being completely Adorkable.
The scene where Bella drinks fresh human blood out of a plastic cup and remarks how good it is was either this or complete Squick for most of the audience.
Jacob's reaction to the name Renesmee.
Come on, nobody mentions Bianca getting dragged off for her grammar and spelling mistakes?
Real Life version—the director for this and Part 2 admitted to USA Today that he had to work closely with Taylor Lauter to keep the Renesmee stuff as Squick-less as possible.