If you complete the "Ghost of a Chance" scenario of Starcraft II, Tosh will become enraged at Raynor during the post-mission communication and will stab a Voodoo doll. It has no effect on Raynor, to Tosh's perplexity, but Tychus finds himself being hit with piercing pain and tossed around the room. Then later when Nova gets ahold of it...
Mission "Engine of Destruction". Tychus shows his love of the Odin in hilarious ways:
"Now how'd I miss this button with a skull on it?"
"Just wake me up when you're ready. I reckon a small nuke oughta do it."
Matt's reaction to Tychus's talks after the first base:
Matt: Does he always talk this much, sir?
Raynor: Yup. Once you get him into a fight, he never shuts up.
After the opening cutscene in which Raynor shoots the TV in the bar out of anger at Mengsk, every time you go to the Cantina (even after moving to the Hyperion), there is a paper taped to the TV that says "Don't shoot the screen."
"P.S. I'll add the cost of the TV to your tab."
Introduction to the penultimate mission:
Tychus: You know, I've been thinkin'.
Raynor: Scares me more than the Zerg.
Several moments from the news broadcasts and commercials:
Kate Lockwell breaking loose and letting out several excited cheers when she's promoted to lead anchor when her predecessor, Donny Vermillion, has himself committed.
The Too Dumb to Live mentality of the AI really kicks in in Media Blitz, where the Odin is implied to be the most powerful weapon of war the Dominion, or perhaps humanity period, has ever created. Doesn't stop any enemy unit at all from running in and attacking you without any concern for their safety. Considering the unit is so big it can knock over streetlights and crush cars just by walking around, it can be pretty amusing to see a lone marine charge in guns blazing at you.
The trailer for the official crossover mod Blizzard DOTA has some hilarious self-aware narration.
These heroes are forced to fight to the death in an endless battle with no purpose other than ladder points.
Raynor got a few quotes in the Hyperion:
"Ahh, I like all the pretty lights."
"I should go for a walk outside... Oh wait."
"That's it. Goin' to have to start pretendin' like I'm wrokin'."
"Standin' around talking to my damn self..."
"What the Hell was I doing?"
When Raynor arrives at the rendezvous point for Moebius and is met with Valerian and the Dominion, Raynor is hailed by them in the subsequent mission briefing. When Valerian tries to posture and refers to him as "Jim", Raynor closes the channel, smirks, then re-opens it a couple seconds later. Cue Death Glare and "I can see why my father wants to kill you."
In the same scene a moment later, there's this exchange.
Valerian: Everyone wonders if I will be as good an emperor as my father. But I want something more: to prove I will be a better emperor, and a better man. Raynor: That shouldn't be hard.
In Supernova, Raynor must get an alien artifact and get out of the planet before it gets completely consumed by its own sun. Guess who choses this moment to show up?
Tal'Darim Executor: James Raynor! We were expecting your arrival... Now you will finally pay for stealing our sacred reliques!