Homestar Runner drops these like toys on a kid's bedroom floor, an analogy chosen specifically because occasionally they pick it up again. They're usually a part of the series' infamous interrupted conversations.
For example, there was a successive run of Strong Bad e-mails where various references are made to "DNA evidence": "And that's when I tampered with the DNA evidence!", "And when I returned, the DNA evidence was gone!", etc.; the final one of these was an Easter egg where Homestar lays still on the couch for several seconds, sighs, and says "DNA evidence." All of this was a set up for the next big cartoon (you can guess the title).
The email "personal favorites" references a number of never-before-seen Strong Bad escapades, like Bubs making a Strong Bad robot out of a Speak-and-Spell and an empty box of Grape Nuts, Strong Bad trying to fly Bubs' concession stand after drinking a glass of soy sauce, Pom Pom and Coach Z getting into a knife fight, and the Cheat trying to eat Bubs' concession stand after drinking a glass of soy sauce.
At the start of the cartoon "Bug in Mouth Disease", Strong Sad is watching a TV program, but we just hear the narrator going "And that's why come Shakespeare was so awesome." Then Strong Bad walks in:
In the Strong Bad Email "4 branches", Homestar somehow got himself stuck in the water cooler at The Office. He explains "I was in Barbados, hanging a picture on the wall..." when Strong Bad interrupts to say "Okay, that tells me everything I want to know."
In "Best Caper Ever", Strong Bad and the Cheat themselves have no idea what they did to cause Homestar to get stranded in the middle of the Arctic Ocean (or how they got satellite coverage of it). All they know is that it started with the Cheat peeing in Homestar's melonade.
In "Decemberween Short Shorts", one short involves Strong Bad writing a letter to a pair of tube socks he knows he will receive as a present. He explains that he is going to tell it some hurtful, unforgivable things, not because he doesn't like tube socks, which he actually does, but because he doesn't want anyone to know that he has a soft spot for tube socks. Why?
Strong Bad: If people found out I had a soft spot for tube socks, it'd be all over. It took me years to live down that Martina Navratilova poster, and I will not go down that road again.
In the E-mail "Bottom Ten," Strong Bad has an in-universe example. Homestar Runner somehow made Strong Bad hug a tree while Strong Bad actively wonders why he is hugging the tree and why he continues to hug it. This wondering doesn't make him stop, however.
The Rick's Minecraft Tales short "Nightmare In Minecraft", the characters refer to something out of context with no warning. Probably justified because it was a special episode to a series which haden't been released yet.
Nancy: Oh yeah!
Rick: Mmh? Oh yeah, that's right! Okey then buckle up!
In Red vs. Blue, Grif mentions Simmons getting into an escape pod after saying, "I'm not going to the Vegas Quadrant." No explanation is further given on the subject, but it is based on something that Simmon's voice actor, Gustavo Sorola, did. In the commentary the cast explains how they had gotten together in Los Angeles (half the cast lived in Austin, Texas) and decided to Las Vegas. Drunk, he said the line above, got out of the van, and ran all the way back to the hotel. The group later found a note saying "See you back in Texas". Of course, no further explanation was given in the commentary either, leading to a double Noodle Incident.
In a more serious example, it's never explained exactly how York lost his eye, just that it involved Tex, Omega, and Wyoming, and that Tex's influence on Omega is the only reason the wound wasn't fatal. What happened is revealed in Season 9, during a training session with York, Wyoming and Maine versus Tex, Maine and Wyoming got serious and started to use live rounds in the pistols instead of the hardening paint. Maine threw a grenade at Tex, who dodged easily, but landed next to York, who was beaten down at the time. Tex used the paint guns to protect him from the grenade blast, but only managed to cover the right eye, leading to York's left eye getting blown out.
There's also the episode where they were discussing how the commandos were all named after states, except "Poor Florida." A moment of silence is then held before continuing the conversation.
Again, this is actually explained in the Season 10 finale: Agent Florida was a Freelancer sent to Blood Gulch to watch over and guard the Alpha. To disguise this, Project Freelancer blew up Florida.
And when Tex comes back as a ghost and reveals she's been watching them
Tucker: So, when you say you've been watching us, you mean all the time?
Tex: Yes, Tucker. And you should be very ashamed of yourself.
"Church, we've got a problem." "A new problem, or did Caboose get his head stuck in the freezer again?" "New one."
Another serious example is the Freelancer break-in on Command. We're only told two details about it: Agent Texas was involved, and it was serious enough to make Command decide to transfer the Alpha to somewhere where it would never be found.
And because of her involvement, something happened or did not happen, ensuring the Alpha would not be rescued. This is because Tex is programmed, for lack of a better term, to always fail at any big endeavors she plans.
To quote Tucker telling a joke/"funny" story to Tex and Caboose: "And I said 'Read it? I already ruined it!" Nothing more is said on this except Tex calling it disgusting and Caboose not getting it.
Now in Season 10, whatever happened to Georgia is becoming one of these. It seems everyone except Wash knows, and he really wants someone to tell him what exactly happened.
In Bowser's Kingdom episode 8, Bowser Jr. showed up on a airship, Hal asked where Bowser's 7 other children went. Jeff responds that they are not allowed to talk about it. Cue Cutaway Gag where the Koopa Kids are maimed in various ways.
Hinted at in an episode of Weebl & Bob in which Weebl is giving Bob lessons on dating:
Weebl: Right. Now you have her at your place. Bob: I have a place? Weebl: Okay, someone else's place. It not important. Bob: Not Hairy Lee's, though. Weeble: No. Not there. That would be terrible. (Both shudder)
In the DSBT InsaniT episode 'The Party', Portica mentions to Koden how she would lend him money and he would never pay her back, then Alex mentions how he would order pizza and, despite the fact that Koden never chipped in, would share with him.
The Ultra Fast Pony episode "Copywrong" opens with Rarity explaining why she needs Fluttershy to model for her. The audience only gets to hear the very beginning and very end of the story, but it's apparently a very convoluted story involving a handicap access ramp, an off-color nectarine, and a wager about the color of the sky.
RWBY: The story of how Professor Port captured a beowolf in his youth is glossed over by the episode to reflect the fact the kids aren't paying attention. The one bit that is focused on is that his grandfather, despite smelling of cabbages, was a wise man. While his grandfather was referenced because his wise advice was relevant to the tale even though the kids don't listen to it, the story behind the unfortunate smell isn't even hinted at.
Dreamscape: Death-T, some kind of sadistic tournament that Keela and Dylan went through. Although Dylan says he will tell his tale of it another day.
The first episode of X-Ray and Vav revealed one of their "heroic" moments involved trying to put out an apartment fire. All we know, though, is that "gasoline made the fire worse!"
In the first episode of season two, we meet Dragonface, who is a big fan of X-Ray and Vav... and who has a restraining order put on him by the two after he did something to creep them out.