This exchange in one of the Riddler's Challenge room.
Hostage: Why doesn't he just tell you what he wants?
Batman: [flatly] ...Because he's INSANE.
Also, in one of the Riddler's interview tapes, Nigma receives a magnificent Take That from Strange, who is explaining the strategy he used to learn Batman's identity.
Riddler: I know you were lying, Strange. There's no way that you could have figured it out! It's some kind of trick. It must be!
Strange: Oh, I use no tricks, no childish puzzles. I simply created a psychological profile of the man most likely to be the Batman, and then matched it against the most logical candidate. I was right, of course.
Riddler: Well, who is he?!
Strange: Ah, but that would spoil the game for you, wouldn't it?
Riddler: You must tell me! I implore you Strange! I-
Strange: Really, Edward? If I could figure it out, it must be child's play for you.
Riddler: But I... I...
Strange: Interesting. Tell me Edward, how is the Riddler like a blank dictionary?
Catwoman: You're right. I think I chipped a nail back there.
That's funny enough, but much later in the game the lines are reversed between the two after Catwoman helps Batman. Batman delivers it pretty poorly, however, and Catwoman calls him on it.
When Batman confronts The Penguin at the museum, the Penguin accidentally (presumably) hits one of his own Mooks with his umbrella in the crotch.
Better yet, if you die in that room (and on harder difficulties you probably will), you get to watch it over and over - and it gets funnier every time.
Batman punching the (significantly-shorter) Penguin off his feet and into a pit while a dramatic chord swells is great for unintentional hilarity.
Even better when you truly defeat him. It's hilarious to just see Batman wail on the little guy at super speed.
This line from the first Riddler Room:
Riddler:Well done, Dark Knight! You figured out how to open a door!
The first time you encounter Harley, she's cartwheeling and back-flipping down to you. She's actually trying to ATTACK YOU. If you counter her kick, you fling her to the side. If you don't? You get hit in the face, and it seems like you're about to have a fight with Harley...until you take her down in one punch anyway.
After she leaves, four of the mooks with her are pointing guns at Batman. The following exchange is priceless.
Mook 1: Just walk away, and everything will end okay.
Tragically, none of the four thugs in the following predator tutorial are designed to be taken out with an inverted takedown (which hangs them from the ceiling).
Not designed to be, no. But you can take one of them down this way if you swing to the third gargoyle on the left fast enough.
If you go to the Iceberg Lounge early, Batman can knock on the door and a mook will peek out. Grumpily asking what you want before realising who he's talking to.
When Vicki Vale reports on Bruce getting involved with Arkham City, she introduces him as "millionaire Bruce Wayne", only to have him interrupt with "It's billionaire, Vicki. Millionaires are so last year."
In the epilogue, Catwoman can talk to various villains/characters. A highlight among them is her conversation with Mr. Freeze.
Catwoman: Well, isn't this nice. I guess Batman found your wife after all.
Mr. Freeze: Yes. My beautiful Nora is now safe.
Catwoman: So is now a good time to talk to you about an idea I had to steal the Pharaoh's diamond from the Egyptian museum? It's really hot there and, well, all this latex really makes a girl sweat...
Mr. Freeze: (Deadpan) Leave me with my wife, Catwoman.
Subjective to be sure, but I always got a giggle out of the boss fight with Ra's al Ghul when Batman smacks his head into the hilt of his own sword.
Any fight with one of the Abramovici twins becomes this if you use the stun gun, which makes enemies flail around with their weapon when hit. Couple this with their size in a room crowded with goons, and Hilarity Ensues.
After you have capture the Riddler, you can be a jerk by standing in front of him. You can also gag/ungag Harley later in the game to hear humorous result.
When the enemies start pulling out sniper rifles, complete with laser sights, upon your return approach to the Steel Mill:
Mook: Nothin's gettin' past me.
cue Batman sneaking up behind them and knocking them out, or just plain pulling them off the ledge.
After you rescued Aaron Cash, you can ask him about Protocol 10.
Cash: Is that some kind of hemmorhoid cream?
Batman: I doubt it.
When you pursue a side mission in the Steel Mill, you come across a powerless elevator with some mooks trapped inside, trying to get it to work. Have fun listening to their panic when you use the Remote Electrical Charge to make the elevator go up and down.
Joker: He's taking you guys to pieces like a puppy in a blender! PULL YOURSELVES TOGETHER!
Batman threatening Riddler informants is pretty hilarious, this line, for example:
Batman: Please don't lie to me. I just cleaned the last informant's blood on my face.
Joker explains to his gang members how he's been cured, but then compares the whole thing to the revelation of the mystery on a TV show. Then he follows that up with, "How come it all ended in a church?"
Solving Riddles in the game will reward you with little bits of backstory about what took place between Arkham Asylum and Arkham City. One of these stories reveals that Joker and Harley actually escaped before being transferred to Arkham City in an attempt to keep away from it. Instead, they stole a boat, and after being chased by Batman, wound up sinking said boat and having to swim to shore, winding up in Arkham City anyway.
Batman's dying, surrounded by assassins, but still manages to crack wise when he get's slapped in the face by Talia Al Gul.
"Hello, Talia."
At the conclusion of the "Fragile Alliance" sidequest to destroy the Titan containers with Bane, this happens:
Batman: I've destroyed the containers, Bane.
Bane: Good.
TYGER*
If you finish the quest after the main game, it'll be Joker henchmen instead.
Bane:Help me, Batman! We must not allow these puppets to take the Titan!
[at least fifteen TYGER guards attack; Bane and Batman take them out in short order.]
Batman: [not even out of breath] As I was saying—
While you can complete the quest in the Playable Epilogue, it's funnier if you do it before the finale, because it means that Batman is at death's door and still easily kicks the crap out of over a dozen trained guards.
In the mission to rescue Nora Fries, if you wait to listen to the Enemy Chatter before jumping the mooks, you can see them playing rock paper scissors, introducing things like guns and dynamite and getting called on it.
It's not only that: they're trying to have a three person game of rock, paper, scissors, and none of them seem to know how to play.
At one point in the game, some of Two-Face's goons discuss a rumor that Catwoman tore the skin off of Harvey's good-looking side, and wonder if they'll have to start calling him One-Face.
After taking the door on a balcony out of the Courthouse with mooks holding the main door shut...
Mook 1: Just hold the door shut and we'll be fine out here!
Mook 2: What if he goes out the back?
Mook 3: There's a back?!
Mook 2: Yeah, Two-Face showed me it...
Mook 3: And you didn't think to mention it until now?!
And another, when approaching the church for the first time...
Mook 1: So do ya think the rumors are true?
Mook 2: What, that Harley used to be a dude?
This may be a Development Gag, as her mocap movements were those of a dude.
When entering the subway to find Penguin's last jammer. Two of his henchmen are discussing if it works underground. One comments that he read the manual which states that it doesn't:
Mook 1: Since when have you been all about reading?
Mook 2: [offended] I read.
Mook 1: Porn don't count.
Mook 2: Screw you.
One of them was apparently a Heath Ledger wannabe, intimidating hostages:
Mook 1 Me, I prefer the hammer. More personal, you know. You can feel every blow. Understand the complexity of the human body as it's deconstructed into a primordial sludge.
Mook 2 That's deep man. I had you all wrong. I was told you just liked hitting people with hammers.
When you enter the smelting chamber a second time (before you encounter a tied up Harley Quinn) a mook will imitate Harley and Joker's voices mockingly, and he's pretty good at it.
Mook (imitate Harley): Oh, Mistah J, please hurt me some more.
Mook (imitate Joker): OK, my dear. Why don't you go out and fight Batman while I make a daring escape...
After the boss fight with Mr. Freeze, you can hear two mooks discussing his kidnapped wife Nora:
Mook 1 Did you see what she looked like? Is she hot?
Mook 2She's in a block of ice.
Mook 1 If you thawed her out, would she be hot?
Mook 2 Way I understand it, if she thaws out, she's dead. But, to answer your question, yes, she's kind of good looking. In a near dead frozen sort of way I guess.
Upon visiting Museum after the end game, you can hear they discussing about what will come up next. One of them wandering if they are going to have Arkham County or Arkham Nation next. At the end they admit that both name sound stupid though.
Mook: What is wrong with the Riddler freak? Doesn't he have anything better to do than leave green question marks all over Arkham City?
It's even better when the Mook saying that is one of Riddler's "undercover" henchmen.
After the Penguin's been defeated, you come across a crowd of his mooks in the subway, getting a recruitment speech from one of the Joker's men. For maximum levels of irony, you can pop out of the grates and K.O. the speaker just as he goes on about how 'invincible' they are.
Even better. One of them, who is playing around with a mask talks about how he will always join the stronger faction, having no loyality beyond that. Said mook is actualy a Riddler henchman.
There's actually a group of unaffiliated (haven't joined any of the gangs) criminals camped out on the roof with a frozen over swimming pool who comment on various story developments as the game goes on. They even manage to survive Protocal 10. Some highlights include them debating which gang they should join up with, and joking with one another about resorting to cannibalism with one saying to another how he's starting to look like a big tasty pork chop...
Apparently one mook didn't listen to Penguin's speech on how they'll be taking over Arkham City because he was on the can.
Hearing mooks talking about their experince in Arkham Asylum during the events of the first game are always a nice call back. Especially when other inmates refuse to listen to their warnings about Batman.
Some inmates can be heard giving tips on how to survive in Arkham City, some which imply an almost Too Dumb to Live mentality among the general population:
Inmate: If you see some strange flowers or plants, it means they belong to Poison Ivy.
Mook #1: So... let's get this straight. You geniuses think that the best way in is to build a boat and sail across a boiling ocean wearing gas masks to stop us getting killed?
The prequel comic shows how Batman uses a nondescript boat to hide the Batboat, in order to come and go to Arkham city at will. Or so he planned - when he arrives the second time, the boat gets blown to hell with him in it! As Batman's flying through the air from the explosion, he calmly notes that "...that worked a total of once."
