8-Bit Theater does this occasionally with Black Mage asking White Mage out and getting beaten up.
Conversely, this strip had Black Mage asking her out with her trying to think of a proper response to get him to really stop asking her, while Fighter, Red Mage, and Thief float off into the sky seemingly because Fighter "slayed gravity".
The various wall posters on Academia. One of them is of Charles Darwin with the label "Chuck D", and another is of the extinct crocodilian Sarcosuchus, labelled "Snarkosuchus".
The Batman: Wayne Family Adventures episode with Zatanna Zatara has the character and Nightwing fighting Copperhead (who's gotten hold of a magic wand). The villain turns Nightwing into a bunny. Nightwing rolls with it and keeps fighting. The rest of the comic shows Bunny Nightwing kicking Copperhead's scaly butt. And it is just as funny as it sounds.
Numerous examples in Bite Me!, such as there being hilarious meanings to french written on signs in the background, or tiny snippets of background conversations, once even between rats discussing political philosophy.
Inverted in EarthBound (1994) fan comic The Chosen Four, thus making it a "Funny Foreground Event." While the main plot takes the back seat, two Exit Mice can be seen chatting. Meanwhile, Ness, Paula, and Jeff can be seen running around in the background in a comedic chase with the rabidly decreasing Guardian Diggers, which is then joined in by Gigantic Ants attempting to avenge their brother Titanic Ant, and then all of the sudden a horde of Mad Ducks and Noose Men.
ThesetwoCollege Roomies from Hell!!! strips. The first one becomes even funnier when you realize the relationship between her and April and how she would be feeling about her right now.
Daughter of the Lilies: The evening after defeating the drath, the group sits and waits while Thistle recovers after fainting briefly. While they talk, Lyra pulls out a compact and starts powdering her nose.
In Freaking Romance, if Zylith's cat Mr. Purrfect is in the background of any scene, he'll be doing something humorously cat-like.
Done subtly in Freefall. During the visit to Ecosystems Unlimited arc, careful observation will show that every time Sam encounters someone with a differently colored security pass, he will steal it and replace theirs with whatever one he has at the time.
In the General Protection Fault crossover with User Friendly, Fooker fights with the person who gave him the software that got him in trouble while Nick talks with his co-worker in the foreground.
A rather common occurrence in Girl Genius, especially when Agatha's little clanks are around.
The non-canon "Oblivious Wand Waving" storyline has this in spades starting with this strip where a guy is turned into a girl complete with clothing changes after drinking a soda.
In this comic, Nanase is running in front of the rest of her gym class without breaking a sweat. In the second to last panel, she's in the background again, meaning she lapped the whole school in the time of a short conversation.
Gunnerkrigg Court: In this strip, Kat and Andrew's facial expressions reference a Running Gag involving Kat's love of birds, while Annie talks to herself in the foreground.
It also happens numerous times once Doc Scratch takes over the narration. For instance thesetwo pages, wherein SS can be seen in the background (and page header) employing atrocious candy bowl etiquette. Then later, while the audience is distracted by Vriska vs. Bec Noir, SS wanders around in the header, casually spreading gasoline around the room, which he then lights on fire.
Inverted as well in that some fans actually forgot to look at the main panels, focused on the Background events, such as Jade accidently killing Dave, and didn't notice Doc Scratch as he beat up Slick with a book.
During Dave's adventures in the LOHAC Stock Exchange, various timeshifted Daves are wandering around in disguises, including one wearing a beagle pusson top of his shades.
Jupiter-Men: While Jackie talks down Rick from beating Quintin, Quintin starts chewing Rick's hand. Rick doesn't seem to notice at all and continues speaking as though nothing is happening.
MegaTokyo has tons of little side jokes and things in its backgrounds. Spotting them all has become a kind of official sport on the forums.
In one of Monster of the Week strips, when Senator orders Mulder to investigate the aliens, there's a picture of Senator shaking alien's hand hanged on his office's wall. It's not as if Mulder notices it.
In the visual-novel styled Morph E, all of the backgrounds in Amical's manor include paintings of Amical. Most of them are normal enough but there are some abnormalities which appear briefly in important CG scenes or distantly in the background of some shots. Examples to date include Amical skiing away from the SkiFree Yeti, Amical as a mermaid and Amical streaking.
Nuzlocke Comics ribs its own Schedule Slip in Ruby's battle with Lorelei, by way of the audience holding a sign that says "UPDATE FASTER".
Speaking of which, although it more qualifies as Funny Background Art, the Coffee of Doom frequently has either weird drawings, or strange menu items, such as "cabbage latte."
In issue 3448, you can see the/a flying roomba chasing a bird above Faye and Bubbles.
Scandinavia and the World: This one has Norway trying to keep Denmark away from the beer while Sister Sweden is talking to her brother.
On this page, Steffi and Undine are having a conversation in the foreground while Techno Blitz stands motionless, scanning the area. Meanwhile, her teammate Swing Blitz sneaks over and waves her hand in her face. When Techno finishes scanning, she nonchalantly chops Swing on the head.
On one page in Chapter 6, while Zoe and Undine are walking to school together, a red-haired girl can be seen hurrying to class in front of them holding a piece of toast in her mouth.
Epic use in Sluggy Freelance (this strip), where the edge of the panel changes the meaning of some background text, which in turn finishes Torg and Sasha's sentences.
Sparklecare: All over the hospital, there are posters with bright colors and smiley faces that display hilariously disturbing messages. Among these are:
"Smile. It only hurts for a second." "Welcome to the Emergency Room! Enjoy your stay!" "Smile! Ur DEAD." "You aren't pretty on the inside. Appearances are FAKE and meaningless."
Following Heather "Spinnerette" Brown accidentally destroyed a hugely expensive genetic modification device thingy, we get to see a panel that's been installed in the lab: "In Case of Heather, Break Glass".
Unsounded: When Sette goes to get a map and a few other things at the Knobbytop way-station every time she's shown again while asking for items the tip jar next to her has fewer and fewer coins in it, in case any readers forgot she's a little thief.
Unwinder's Tall Comics. In this strip, Howard is in the background, apparently spewing flies out of his mouth. In this strip, Moist Rider can be seen working in the background of Howard's coffee shop, which ties in with that strip's Alt Text, "Howard won't hire anyone he didn't create."
The Wotch has a kid on a skateboard who runs into telephone poles a lot. See here. He gets a slightly more important role here.
Thisxkcd comic is a simple pun on the phrase "The best defense is a good offense." Appropriately enough, the thesis being defended is apparently "The Evolution of Threat Defense in Mammals".