Before hiring Niko for some jobs, Elizabeta warns him that she won't be as easy to work for as his previous boss Manny Escuela was. Niko disagrees. Why? "I won't have to listen to him talk!" Everybody has a good laugh over his quip, and chances are you'll be laughing along with them.
When Elizabeta starts freaking out because she thinks the cops are on to her, Manny busts in with his camera crew, spewing obnoxious preaching at Elizabeta. She promptly pulls out a gun and shoots him in the face. Almost everyone playing through at this point will be rolling with laughter at this, since, well, it's Manny.
This cutscene, also involving Manny and Jay, his God-awful camera man.
In typical Grand Theft Auto fashion, the radio is littered with hilarious spoof advertisements and talk shows.
Most of the intros to Brucie's missions, which usually involves him being stupid and either hurting himself, or getting Niko to hurt (or threaten to hurt) him. Also, the intro to the mission where Niko has to pretend to be gay. Including the profile that Roman sets up for him. Seeing Niko's mugshot-worthy face with the phrase "I just want to be wrapped in strong arms" is hilarious.
Niko: Brucie, I don't need to see your balls. I'm good.
Despite being a hardened criminal and killer, Niko still makes the types of jokes a 12 year old would make regarding Brucie's balls. A notable one is when he calls Brucie to inform him he failed an Exotic Export mission.
Niko: Brucie, are your balls OK? You sounded real mad.
Almost all of Niko and Packie's back and forths with a Bound and GaggedGracie Ancelotti in the mission "Diamonds Are a Girl's Best Friend" are gold. Actually, almost any time Packie is involved in a mission, or even just in the car, with Niko, it's usually pretty hilarious.
During the mission "Waste Not Want Knots", while trying to steal from The Mafia:
Packie: There's got to be a pizza parlor on this island coz I ain't never seen so many Italians!
Listening to the Tuff Gong radio station (you know, the reggae one) causes some pretty hilarious soundtrack dissonance. A high-speed cop chase underlaid with somebody singing mellowly about a girl who likes to party and have a good time, or Bob Marley's "Three Little Birds". Then you'll hear the host warning the listeners not to buy the Excelsior razor, saying that "you might cut off ya nose".
The pedestrians and the gang members will make you fall out your chair laughing!
The fat cops, the Alderney or Redneck cops, the Hispanic cop, and the N.O.O.S.E. is ABSOLUTELY this trope. Seriously, you will laugh your ass off no matter what they do or say, but here's some memorable gems.
Alderney Cops: You have the right to shut the fuck up!; Okay, so let me repeat your message, BLA BLA BLA, LULULULULULULUH!!; This is Eagle, I have confirmation on chicken shit;
Niko's summation of not-so-stable gangster Ray Boccino.
Niko: "He's a rat doing an impression of a man."
Drug dealer Playboy X needs the main character Niko to kill someone who has been talking trash behind his back. His description is... unhelpful.
Playboy X: Son ain't too diesel or nuthin', but he a regular lookin dude, knowwhatimean? And he don't flash his guac too much, but you can see it in his eye, he a hustler.
PBX: Homie ain't too brollic, but he ain't scrawny neither, and he beats down on him a little you dig? I mean, he ain't too bummy, but he grimy, too.
Niko: ...so he's the average one?
PBX: Look, he brown skinned B, motherfucker be rockin' baggy clothes, all that, jewels and he stay fresh with the clean sneakers, knowwhatimean? But sometimes a bandanna.
Niko:: Look. I need more than that to go on.
PBX:: Jesus. Here, take this [camera phone], head down there, take a photo, send it to me, and I'll point out which one of them motherfuckers it is.
Niko is looking for the guy who sold his army unit out. His first lead is some Florian Cravic. Ray finally gets a lead on him, and he takes Roman on his little revenge quest... Only to find that not only he's not the guy Niko's after, but he also changed a lot after going to America, changing his name to Bernie Crane, becoming a lifestyle instructor (as he says) and having an affair with... the Deputy Mayor, Bryce Dawkins. It's funny because you get Flamboyant Gay when you expect some kind of shady, dirty-looking dude as a traitor.
The cutscene after the very first level. While a lot of it is funny, CMOF has to go to when Niko starts giving an introspective, very serious narration on his time in Serbian Army, which sounds like it could have come right out of the mouth of Solid Snake. Roman's response? He falls asleep.