Hm, I have a lot of these, and I've been linked excellent stories from various /tg/ threads. Let's see.
There's the time a friend of mine in an rp I was not in turned a tank into a group of velociraptors with chaos magic.
There's the time my char Wyatt got eaten by a dragon (actually a metal robot powered by a captive god, but...it's complicated). This resulted in another party member realizing just how much he cared for Wyatt, and asking him out. I should note that Wyatt has been consumed by multiple things including a jelly, a toon shark (more than once -- it makes sense in context) and said dragon. Oh, and a toon...was it a squid? Octopus? Something like that.
There was that time two characters had a surprise wedding. ...Let me explain. We had some timeline stuff and history got changed, but people from the old timeline didn't have the memories of the new timeline. /Lots/ of things changed, including various characters' temperaments in the past, but it didn't affect the transferred characters. So apparently the parents were worried about...I don't even remember, possibly an illegitimate heir (groom was an earl and it mattered), and apparently the couple was less cautious about taking precautions. Also they (their new timeline selves) had been involved in planning said wedding, but the two from the old timeline didn't know about it, because they hadn't gotten around to doing it. So yeah...they were surprised by their own wedding.
There was that time we had a fangirl get access to the Tower, the seat of Harold's government. And by fangirl, I mean she shipped the President with his Head of Intelligence. Apparently there's a club. And fanfiction. ^.^;;
We have in-universe shipping in the current campaign too, but it helps that the party became nuclear terrorists by accident (crazed and vengeful spirit had a nuclear warhead we didn't know about and was trying to blow up a government meeting. We stopped her, but got in trouble anyhow) and then because we were facing a lot of difficulty because the nuclear war that the planet is still recovering from was only two centuries ago, a documentary was made about the party showing them as people and what we're trying to do. ...We're totally vigilantes though.
That one time my character became the avatar of a goddess by accident. She's not even religious!
It's not happy, but the time my one character got killed and then resurrected. Honestly Maxwell the squishy and stupidly altruistic doctor and sworn pacifist and Malie the invisible soul-eating demon who thought he would be easy to manipulate and ended up falling for him are an adorable couple. <3 There's also some ethical struggling because...well, pacifist plus souleater. ^.^;
There is the time the party faced snow fairies (nasty critters that will drive you insane or just kill you outright). They made the ground slippery, but Kat has high agility, so she actually did /better/ because her checks were so high they gave her bonuses to other actions. She has a low fight stat, but still managed to do four shifts of damage (a very solid blow) to one of them. With a jacket. Because it's totally an area attack when you throw a large, heavy winter jacket over something the size of your finger.
Then there was the time she rammed a dragon. With a tank. Of course it ended poorly because I asked to compel her trait "didn't think it through", but it was fun.
That one time Nikki (Kat before she had her name change and lost her nekomimi traits for a different worldsetting) hijacked a tank.
That time the same character accidentally turned two other characters into gods (powerful artifact designed to make gods. They were being careful, but they were wary of her, and accidentally got too close. Oops!)
Just about anything that involves Nikki/Kat is bound to be fun, actually. The whole adrenaline-junkie doesn't-think-it-through deal makes for an excellent way to get into trouble, and her love of pranks is icing on the cake.
