Powers up: "Now I'm better at doing whatever it is Wolverine does!"
Also, Deadpool haggling a SHIELD agent over how much money the agent will give him for freeing him.
"Stretchy man suggest Hulk release anger with words. Hulk call it 'Hulk-ku'"
"Hulk smash wide load sign;"
"Not appreciate insult;"
"Hurt Hulk's self image."
Or:
"Hulk break lots of things
"Everything make noise when broke"
"Hank wrong about mimes."
Or the best:
"Hulk want hug kitties;"
"But they so easy to squish;"
"Hulk live in cruel world."
The recording Fury left for Stark:
Computer: (Fury is trying to activate the self-destruct protocol for Prison 42) There is not enough free memory to run this program. Quit one or more programs, and try again.
Fury: Stark... your IT department sucks.
Some of the early boss battles can be this when it's 4 on 1 against a fairly easy foe. Bullseye in particular will end up getting curbstomped by four heroes in a pretty hilarious image.
During the Tinkerer's boss fight, hit him with Hulk's Takedown move and try not to laugh as this giant monster tackles a non-powered old man and punches him to the ground.
An announcement comes over the PA in Stark Tower saying "Warning, a small thermonuclear device has gone missing, and Deadpool was last seen in the weapons lab". Later on, you can hear one announce that Deadpool has returned the device - it didn't make a very good basketball.
The Stark Tower PA is good for a lot of funny, from Johnny Storm leaving a prank "Happy 65th birthday, Ben Grimm" announcement to reminders that "Miss Bambi and Miss Heather" are still waiting for Tony in the main lobby.
Deadpool will make an interesting comment if you have him in your party when you go anti-registration.
Commander Maria Hill: You don't know what you're doing!
Deadpool: Par for the course, crazy lady! Besides, I can always go the other way on my next play-through.