Once, my brother and I were playing, and my brother was stuck in the Dreamlands. I read the encounter card and it said, "At the south gate of Thran, you are stopped by a red-robed sentry until you can tell three dreams beyond belief." Just for fun, I played the part of the sentry and said, in a deep scary voice:
"Halt! You may not pass until you tell me three dreams beyond belief."
"A rap battle is also acceptable."
We then proceeded to have a Cthulhu-themed, very badly improvised rap battle right then and there.
Encounter at the bank: "A little old lady stands in front of you in line counting out a bag of pennies to deposit. Lose 1 Sanity."
Made even funnier if you think about what it would look like in-universe if you happened to hit 0 from this. This Troper had it happen to him, which immediately resulted in a lot of jokes about surviving three Other Worlds and this was the thing that broke my character.
An encounter at the University can result in you giving a guest lecture about the Mythos...only for everyone to conclude you're off your rocker and ship you to Arkham.
My second game ever was with two of my friends. One of them (playing Harvey Walters) went to close a gate at a location. She didn't have enough clue tokens or an Elder Sign, so she couldn't seal it permanently. She went there, killed the monster sitting there, went through the Other World, killed another monster that went there in the meantime and closed the gate. In the next Mythos Phase, a gate opens right where she stands. So she kills the monster, goes into the gate, wanders through the Other World, comes out kills another monster and closes the gate. Then another gate opens at her location. By about the fourth or fifth time this repeated, we were imagining Harvey just running through the Other Worlds ignoring everything and then kicking the cr*p out of the Eldritch Abominations. But the Crowning Moment of Funny was when my other friend had an encounter at this location and found a heap of skeletons sitting there. We all knew: Those were the victims of Harvey 'Monsterslayer' Walters.
One of Wendy Adams' abilities, Minor, prevents her from getting a bank loan. However, it does not stop her from becoming the Deputy of Arkham. What makes this even more hilarious is that "Skids" O'Toole has a similar ability, Criminal Record, that does stop him from getting a bank loan or becoming deputy. So we can conclude from this that a homeless little girl is more trustworthy than a former criminal.