I'm obviously asking as a gamer who has seen the quarterstaff in a billion games since I was little. I have read in various places they were not used the way commonly depicted by both games and kung fu movies and so on (that they were used more like blunt two handed swords for beating), but I was really curious that if there was a European common use for them, as they show up so often in games with pseudo-European settings.
I can't imagine them being popular on a medieval battlefield, so what was their actual history or historical use?
The staff or quarterstaff was generally the weapon of poor men, monks, or other people who didn't/couldn't carry relatively available weapons like a spear or axe. A traveler might carry a staff, especially if he wasn't expecting too much trouble. A pilgrim walking from Cheshire to Canterbury, for example. They also didn't violate any laws that towns might have on bladed weapons. (Think Gandalf at Théoden's court, keeping his staff)
You're actually right. The common image of the quarterstaff being gripped at the third-points and used to bludgeon with both ends is false, and dates from the Victorians. The Renaissance fencing master Joachim Meyer wrote a treatise on using the weapons of his time, and the staff was among them. It is shown being gripped much like a longsword, with both hands toward one end.