Ezio has a rare moment of embarrassment when discussing his 'self-expression' with his own mother:
Ezio: I have plenty of outlets!
Maria: I meant besides vaginas.
What really sells it is the expression on Ezio's face and the tone of voice he uses when he says the last line. It's like listening to a 15 year old telling his mother to shut up when she talks about embarrassing stories to his girlfriend.
Any cutscene with Ezio and the prostitutes is guaranteed to cause chuckles.
"I've always had a soft spot for women in distress."
When Ezio gets his first assassin's blade, Leonardo brings up the fact that he'll have to remove his ring finger as a 'sacrifice'. Leonardo then grabs a large butcher's knife and bringing it down very close to said finger, before revealing that Altaïr had found a way to avoid the finger removal and that he'd just been amusing himself.
One of the Assassin's Tombs lets you eavesdrop on a pair of guards, one of them given to incredibly paranoid ramblings, much to the other's annoyance.
After pestering Shaun Hasting for conversation, he eventually runs out of dialogue, and just starts greeting the player with "Hello, Desmond. Go away."
Somebody was having fun writing Caterina Sforza's speech taunting her children's kidnappers, which gets more obscene, more gruesome and more hilarious as she builds up steam. The best part is that when she really hits her stride, the Animus just gives up and stops translating. Not that it matters if you understand Italian or not; her tone gets the point across beautifully.
It should be noted that most of that speech was real - as in, something she actually said during a siege, obscenities and all.
Watch it in all its hammy glory here (the good stuff starts at 7:35).
On a related note, Shaun refers to Caterina as a "lunatic warrior mother".
One of the best moments is when she yells "Go ahead, take my children! I have the instrument to make more!" and then flashes the Orsi brothers. And the best part is that she actually did this!
Eventually you're tasked with rescuing her kidnapped children. Bianca seems to have inherited her mother's fiery personality spending her captivity yelling at her captors about how they don't have enough men to hold her and other things. Ottaviano, meanwhile, just whines about how he has to go to the bathroom much to Ludovico Orsi's annoyance. It's enough to almost make you feel bad for Ludovico. Almost.
Earlier, Machiavelli informs Ezio that Caterina's husband was working for the Templars, to which Ezio says "I'm sorry to hear that." The funny part is Caterina airily replying that he shouldn't be because she had him killed. There's audible terror in Ezio's voice as he replies.
Bartolomeo, Boisterous Bruiser and Large Ham, whose speech in prison is nearly as funny as Caterina's. Other moments of his include being unsure whether to kiss Ezio for freeing him or slap him for taking so long about it (neither option enthuses Ezio), rampaging through the streets of Venice beating guards to death with a broom and bellowing about his need to smash heads, and introducing Ezio to his gigantic sword, Bianca, by pointing it directly at Ezio's nose.
Bartolomeo: Ezio, meet Bianca. Bianca, Ezio!
Ezio:(carefully moving the point with his finger) ...Charmed.
The "meeting" with Bianca is later recalled in Brotherhood, when Bartolomeo calls for his wife and Ezio asks, "Did you check behind the table?" To Ezio's surprise, this time around the wife is an actual live human woman.
Each and every time Ezio uses a springboard in Oltrarno District.
They also mention how people have started climbing buildings for sport (including Ezio), and say that though it isn't illegal, it's all fun and games until somebody breaks a leg...
Ezio, during the Nightcap mission early on in the game, makes a late-night calling to one of his many girlfriends, Cristina. When she invites him in through her bedroom window, we are treated to this exchange:
Cristina: Only for a minute.
Ezio: A minute is all I need!
Cristina: Mmm, indeed.
Ezio: Wait, that came out wrong...
As part of the tutorial, the player is introduced to fleeing from enemies when Ezio and Cristina are caught by her father. As Ezio runs for his life, he desperately pleads for mercy, claiming that it's Not What It Looks Like (even though it most certainly was), including this gem:
Ezio: I'm mostly innocent!
Jerking the NPCs around can result in funny dialogue:
Minstrel (while being grabbed): Let go of me! You have no appreciation for the arts!
Minstrel (while being grabbed again):''' Was my melody...not to your liking, signore?!"
Minstrel (if jostled into dropping his instrument): But, but I love you, noble one!
Female NPC (when frightened by a death and running away): The Lord is my shepherd! THE LORD IS MY SHEPHERD!
After Ezio kills a guard who was beating Leonardo, he asks what he should do with the body. Leonardo's response is to take it inside and "put it with the others". Granted, there turns out to be a reasonable explanation, but the line can still get you if you're not expecting it, and Ezio and the audience have pretty much the exact same reaction.
When Desmond views the memory of Altaïr chasing Maria, he makes a disturbing realization.
Desmond: Wonder what he wants with her... Altaïr and Maria start kissing
Desmond: Whoa...Alright, wasn't expecting that... Cut to Altaïr and Maria on the floor, with Altaïr jumping off the tower
Desmond: Wait a second...Why aren't I following Altaïr? I'm stuck here with Maria. Oh shit! That must mean... note i.e. he just witnessed his own ancestor's conception
Bribing a herald to keep quiet about you for a moderate sum to lower your notoriety—and then stealing the entire bribe back the next second.
All of Ezio's taunts are rather amusing, but some against Brutes are downright hilarious:
Ezio: Can you see anything in there?
Ezio: Diarrhea got you stuck? Try leeches!
Ezio: Fatti sotto, porco! (Come on, pig!)
Ezio: Come on, you fat pig!
Ezio: Well, you’re certainty well fed!
Shiv someone with the poisoned knife, then do the same to someone in the inevitable crowd that gathers. Instant mosh pit.
The minstrels. When they're running in front of you while trying to escape guards they're annoying, but if you stop to listen to them for a while, a combination of terrible singing voices, bad lyrics and ridiculous accents makes them hilarious in a So Bad Its Good way.
If Ezio hangs around long enough for the guards to discover the latest dead body, they'll start to question him about it. Simply standing there innocently and saying nothing (while incognito, anyways) will eventually prompt them to walk away, questioning your intelligence as they go...