This is based on opinion. Please don't list it on a work's trope example list.
Nightmare Fuel / Freeman's Mind
In episode 8, Freeman gives us this horrifying anecdote:
"This window kind of reminds me of when I came home from school and there was some dead guy stuck in the smashed window of my apartment. He'd been trying to break into the place, but instead gutted himself on the insulated glass. That was not fun trying to explain that to the police."
Not sure what's more disturbing: How gruesome that story is, or the fact that Freeman found it to be more irritating than anything else. Then again, you could get some Alternate Character Interpretation out of this: Maybe Freeman was once more normal and stable, but the psychological trauma of things like that happening turned him into a dysfunctional lunatic with next to zero empathy.
Alternatively, he was already so crazy that he didn't really care. Or, he's in denial about smashing a guy through his window in a fit of rage.
There's also the fact that this has probably happened to people in real life. In fact, knowing Ross* (the first Freeman anecdote in the show — the squirrel in the power lines — actually happened, just at a different school and to one of his professors), it might be based on something he heard in the news.
Gordon Freeman's basically a deranged, unstable madman, who can be victim of weird episodes where he loses control of himself. For example, the "Class is in session!!" or "No comment!!" parts in episode 9. Sure, they were cool and everything, but what if he had other episodes like those in the past? Or if he could have more in the future?
One Bullsquid gives Gordon some, and we get to hear about it:
Gordon: Yeah, that's right, moan! MOAN! That noise is exactly what I'll be thinking about when I try to go to sleep tonight! And I'll be dreaming about you sucking out my eyes with your tentacle face, while I'm nestled up against a stack of rotting corpses, then my intestines will burst with insects crawling out of them, then the screaming...
A lot of Gordon's inner monologues qualify, given his Cloud Cuckoolander mindset. Here's a few examples:
"Hey, that's a ladder! That means this is legit; this might actually go somewhere! I mean, it probably leads to a room filled with poison gas and a bunch of dead people that look just like me, but I don't know that, so there's room for hope, I guess."
When he does fall in, he panics when his Geiger counter starts going off and he sees a security guard. "RADIATION. DEAD BODIES."
"If any of these worms get in my hair, I swear to God I'm just gonna freak out. Yeah, worms get in my hair; the power fails and the lights go out; then some old guy with a raspy voice starts laughing and poking me with a stick. That would complete the experience."
"I was expecting to look down there and see this giant eyeball looking up at me, angry at me because I blew off its eyelashes or something, then the whole building starts shaking and I guess I'd just ball up and cry, because what do you do when something that big wants to kill you?"
His theory that the tentacle monster in the rocket test chamber is actually just the hair of a larger monster.
At one point he theorizes about killing a security guard and using his intestines as rope. He only decides against it because it would be too slippery.
Freeman's all-too-plausible theory that the "reactor" in Lambda Core is nuclear in nature, and that it's on the verge of meltdown. A potential China syndrome is nothing to laugh about. Even Chernobyl never got that far.
Freeman's breakdown when he first gets to Xen. It's definitely funny, but also disturbing considering how genuinely afraid he is. Not to mention the fact that he starts contemplating suicide.
Freeman's reaction to the Nihilanth is the worst in this regard, as it's surprisingly dark for this series. Freeman begins breathing heavily, and you can hear his heartbeat. Then he starts screaming, and roll credits.
And what happens if Freeman doesn't take the G-Man's offer? He gets teleported to a world of G-Men monsters with no ammunition.