Standard spoiler trope warnings apply.
For StarCraft I, see here.
For Wings of Liberty, see here.
For the multiplayer, see here.
Watch the Heart of the Swarm trailer and at about 1:20 see Kerrigan load her rifle and point it at her enemy with a ridiculously cute face, with her own voice saying in the background "The killing will never stop until Mengsk is dead!"
In the first mission, Valerian tests Kerrigan by asking her to control a drone and use it to build a zerg base. After warning him for a moment that this isn't going to end well, Kerrigan suddenly produces Zerglings, invades the zone with them and wrecks the labs... then brings the zerglings back to cages. She wasn't rebelling or anything, she just wanted to screw with Valerian to teach him thatEvil Is Not a Toy.
Valerian: Maybe next time you could try to convince me without wrecking half the lab!
What makes Valerian's line go from funny to hilarious is two things. First, the total deadpan delivery of the second line, the tone equivalent of the Flat "What.". Second, one of Valerian's lines regardless of what you use is "This isn't a game, Kerrigan!" If it comes on the heels of that line though, the exchange goes together perfectly to make him sound annoyed that Kerrigan is taking the idea of wrecking the lab like a joke.
Critters are back with humor. The ursadak calf's description when you hover the cursor over its wireform reads "benign creature that sautees well with butter".
Said zerglings come into play later when the pair has to escape through said labs and run into several waves of the test run zerglings on the way out.
Nova's small contribution to the story is not funny by itself but she did steal Kerrigan's man right from under her nose, which is a little detail the shippers and fanfic writers will probably have a ball with.
When you fight the Primal Zerg, they have a number of units that look and act nearly identically to your own, which most players will shrug and chalk up to Gameplay and Story Segregation to make the devs' lives easier. Actually, the Primal Zergstole the designs, despite you only being on the planet for a day at this point. Abathur is hilariously pissed.
(Kerrigan asks for an explanation. His anger becomes more and more apparent as he explains himself. In its full monotone glory all the way.)
Kerrigan (teasingly): Abathur, are you upset?
Abathur (livid): UNACCEPTABLE!
Really, all of "With Friends Like These" is a bit of a breather (Relentlessly bleak Zerg campaign getting you down? Here, have some wacky Terran antics!).
Any and all interactions between Matt Horner and Mira Han. Especially when he realizes they need her again.
Mira: Matthew, don't think I will make this easy on you. Matt: When have you ever made anything easy on me? Mira: I thought you liked it rough.
Not to mention Valerian meeting Mira:
Valerian: Mira Han, this is prince Valerian. Do you read me? Mira Han: Of course I do, princess. I know you're working with Matthew. Put him on, please. Matt: (walks into the camera range) ... hello, Mira. Mira Han: Matthew! You never write, you never call. It's almost as if you don't care!
Especially when Valerian starts catching up with the history the "pair" shares.
Mira: (ridiculously out-of-character pouty voice) Oh Matthew, I hate it when we fight... Valerian: Do you two have some kind of strange history? Matt: (growls) *Don't* encourage her.
Poor Valerian's endless bemusement at the roughnecks he's thrown in with. After destroying the pirate cruiser and snaffling its toys for the Hyperion:
Swann: They had an electric field generator. This baby overloads enemy craft, disabling them for a little while. Valerian: Let's get it installed, Chief Engineer! Swann: It's already online, Scooter. I do good work. Valerian: Scooter?
Stukov: Let's recap. I was betrayed and killed, shot into space, captured by the zerg, resurrected and infested, cured, given to Moebius to research the protoss cure, and was instead experimented on as the cure slowly failed. Everyone up to speed? Good.
Abathur's description of the Raptor has a paragraph about their leaping abilities, which let them scale cliffs and leap to attack foes. Then, at the bottom, as an afterthought:
When Abathur admits to Kerrigan his concerns about Stukov's infestation, he explains that its complexity is second only to Kerrigan's Primal transformation, yet appears to have been specifically engineered in a way Abathur cannot duplicate. Kerrigan correctly guesses Abathur dislikes the idea of someone being better at genetics than him, and Abathur declares that such an enemy would be impossible to defeat and suggests they surrender and submit to them.
Kerrigan, of course, shoots this idea down on the spot.
Which is an epic Brick Joke from Wings of Liberty.
Until Zagara learns her lessons about Vision, Kerrigan keeps making her go to Abathur to get additional cerebral capacity spun into her DNA, so she can understand what Kerrigan has taught her. By about the second time, Zagara expresses a reluctance to go. What sells it is her plaintive complaint:
Zagara: His work is painful.
Kerrigan: His work will help you understand vision.
Hidden in the sound files are outtakes which are quite hilarious including Dehaka parroting Kerrigan’s lines from the cut scene where she thinks Jim has been killed off screen, Raynor saying “game over Darling” then asking about Legacy of the Void, and Abathur rapping.
Abathur: (Laughing) Must consume, acquire essence, improve swarm, bitches, bitches. [Abathur starts to beatbox] Horner: (Totally Deadpan) Sensors are picking up things we can jack. Raynor: So who's up for Legacy of the Void?