Well, in addition to the usual trivia about medieval weapons and armour and obscure English vocabulary, like knowing what's a Dacian falx and being able to use words like 'verisimilitude' in everyday conversation...
I used to know an obscene amount of stuff about the development of guns during the 19th century, though I've forgotten most of it. I still do remember that LeMat is really, really cool.
For a gnomish gun fetishist PC, I did some studying on early firearms.
For a gnoll ranger, I researched hyenas and can tell the tomcats aren't the only ones with weird stuff down there.
Via my hobby, I've also learned a lot of stuff about American legislation that I probably wouldn't otherwise know. Heck, I know more about American laws than I know about Finnish ones. Of course, the stuff I know about American laws is the kinda stuff I don't ever want to need to know about Finnish ones...
By the way, I also used to be able to list the men accused at the Nürnberg Trials and their sentences, plus the order in which those sentenced to death marched to the gallows. This isn't strictly due to gaming, though, more because I strayed while studying for a history exam. I did receive top marks from that exam, though.