Two fictional universes have a character known as Q.
The first appears in James Bond, the Quartermaster originally known as Major Boothroyd. He supplies 007 with gadgets, weapons and vehicles of varying plausibility, often irritated by Mr Bond's flippant attitude. Q was played in most of the films by Desmond Llewelyn, who will be synonomous with the character for almost all long-time Bond fans.
The second is from Star Trek, appearing in the first episode of The Next Generation. Played by John DeLancie (who, incidentally, my good lady believes is a dead ringer for the man who lives across the street: I can't see it myself...), this Q is an all-powerful being who can manipluate time and space. Being all-powerful, he uses his abilities to wreak havok and generally annoy people. So annoying, in fact, that a character who ran off with him in TNG appeared in Deep Space Nine (I know, I talk about it a lot because it's on TV every weekday at the moment) attempting to get away from him. Hilarity (sometimes) ensues.
I used to joke about what would happen if the two Q's swapped places. Bond films would be considerably shorter - "007, we have discovered there is a double agent in our midst, we need you to... oh, don't bother. Q's already sorted it." - while Star Trek would be blessed with a kindly, sometimes frustrated, old man - "Pay attention, Captain Picard."
Finally, back on the subject of DS9, Q is also for Quark. He's my second favourite character in the Star Trek universe, after Doctor McCoy. I was going to post extolling his virtues, but I'll save that for another time, as I'm sure I'll go on a bit...