There are several in The Room. The most infamous being:
Mark: "How was work today?" Johnny: "Oh, pretty good. We got a new client at the bank. We'll make a lot of money." Mark: "What client?" Johnny: "I can not tell you, it's confidential." Mark: "Oh, come on." Johnny: "I can't. Anyway, how is your sex life?"
Played as a joke in Time Bandits when Robin Hood asks a dwarf bandit how long he's been a robber. The robber replies, "Four-foot-one!" A confused Robin stammers out, "Four-foot-one? That... that... that is a long time, isn't it?" before moving on. Since the bandit is an ageless, time-jumping angelic being, he apparently decided to simply supply his height rather then try to answer the question.
Pablo (Spanish accent): One time I threw a stick at a monkey...
Subverted and Lampshaded in Scrubs. J.D. always appears to the other characters to be saying these, because he constantly imagines something related to the issue at hand and then makes a comment about his fantasy that winds up sounding totally nonsensical to the other characters. Generally, the longer and more elaborate the fantasy, the more removed his comment will be from the situation that triggered the fantasy in the first place.
Precious Roy: This is Precious Roy, and you kids better pay for that lap dance!
Sifl: Precious, we're talking about the Civil War Corpses...
Precious Roy: APPLE... CIDER!
Sifl: ... What?
Precious Roy: Suckers!
In the song by Andrew Huang, each word is a non sequitur, even though there never had been a real point to rabbit-trail away from other than the statistics at the beginning. This how many of his other songs tend to be.
In Jack Sparrow by The Lonely Island, the guys have a recording session with Michael Bolton, who mentions at the beginning of the video that he had just finished watching a marathon of Pirates of the Caribbean. They all proceed to sing about being gangsters at a club...until Bolton goes off and starts singing about Captain Jack. It eventually descends into completely-unrelated mentions of Forrest Gump, Erin Brockovich, and Scarface, one after the other.
Andy Samberg:(annoyed)...Turns out Michael Bolton's a major cinephile...
Throughout the series, NPCs can have conversations with each other. However, these conversations consist entirely of random voice clips, so they are literally nothing but a series of strung-together non-sequiturs.
Scarface: The World is Yours is stuffed with lines of dialogue. That sometimes doesn't flow together quite well. Tony would ask a girl to clean his pool and she demands they go shopping. Then he asks why she hangs around all the time, even though he invited her to live there. Then Tony starts talking about murdering his enemies, sometimes even after they are dead.
raocow: You are not the unicorn of my love, football Charlie! You are merely a pawn in the great game that we like to call... Mario World. Although you are one of the important pawns. You are like, that one pawn in the middle that you start in the beginning of the game in order to, like, capture the whole world and stuff.
Nappa from Team Four Star's Dragon Ball Z Abridged says one of these with nearly every sentence. Much to the confusion and frustration of everyone around him. It is even lampshaded in the Dragon Ball Z Kai Abridged video.
Nappa: Hilariously derailing one-liner.
Goku, though not as frequent, at times does this as well.
About 50 percent of everything Ed says from Ed, Edd n Eddy says is a non sequitur. Often, when he's asked a question, his response is "buttered toast" or "gravy" and he randomly shouts "I love chickens" even when there aren't any chickens present.
Gerald: (singing, after everyone else has stopped)Courteney Cox, I love you; you're so hot on that show...
Kyle: Dad... Dad? We're singing about a dreidel.
SpongeBob SquarePants has some as well. One of them involves SpongeBob trying to get Mermaidman and Barnacle Boy out of the retirement home. He attempts to reason with them, then Mermaidman gets fed up with it and says the following:
Mermaidman: "If you don't get out of here, then by the power invested in me, I now pronounce you man and wife!" Orderly: (walks into the retirement home's main room) "What is going on in here!?" Mermaidman: "You may kiss the bride!!!"
On Clerks: The Animated Series, while trapped in the freezer Randal sees an old lady shoplifting and he yells "The weeds of crime bear bitter fruit, you old hag!" We then see a flashback to the last time he said that, where it comes out of nowhere and makes no sense.
Seen on a button:
American Non-Sequitur Society—We don't make sense, but we do like pizza