Funniest single thing I've heard was on a Teamfortress 2 server, someone on our team decided that it was karaoke night, and that he would do requests.
It wasn't as annoying as it was amusing, he was an awful singer, but was very well aware of it. Some of the requests that people started naming just made it all the funnier though as people requested odd random songs by various female singers and so on.
Another was this...bizarre one I heard on another Teamfortress 2 server. One of the players involved was a Sniper who killed one of our Scouts. What ensued was an hour long vendetta with the Scout talking about how he was going to kill the sniper with his bat, how much he would enjoy it, he needed help, how this had to happen, how the sniper had to pay, things about the Snipers mom, etc..
Due to poor level design and a lack of a timer on this custom map, the match just dragged on forever and neither team would make any headway. The only real voice chat after a while since we had all given up was our Scout's need to kill this Sniper (he wasn't being totally serious anymore, but it was one of the few ways to try to get enjoyment out of the map). Ended up having several people join the crusade, including Medics who provided Ubers to try to get through the lines.
Strange, but brought some much needed amusement to an awful map.
