yes
Do you ever sacrifice your queen?

Not with nothing in return to stop a mating attack, I'd rather resign. I'd do it for checkmate obviously, or even for a knight/bishop/rook to enter a winning pawn endgame.
I just did. After a series of blunders by me in the beginning, followed by some better play culminating in opponent hanging his queen, we came to the following position. I decided my chances in endgame were much better, even with his rook, so I sacced my queen.
In the event the opponent blundered soon after and resigned, but it would have been interesting to play out the endgame.

I remember when I was a teen and first learned chess. Nothing ever seemed more dramatic than some of the great games...Q sacrifice and then a bold, daring finish.
I have done this too. On occasion. I certainly wish that I could do it more often. To me, this is the most dramatic and fun way to win.

I just did. After a series of blunders by me in the beginning, followed by some better play culminating in opponent hanging his queen, we came to the following position. I decided my chances in endgame were much better, even with his rook, so I sacced my queen.
In the event the opponent blundered soon after and resigned, but it would have been interesting to play out the endgame.
Bxe5 does not deserve any question marks, it is the best move in the position. Your right it hardly affects blacks overwhelming advantage. White should've resigned many moves before.

Only once for me...I made the sac for a 2 rook exchange...but it was rather a tense struggle to fight off two rooks...in the end I was able to come out of it with a draw. I actually made the sac to experience such a fight, since I would have never done such before...and only did so after seeing the Masters exchanging the Queen for 2 rooks...I believe it was Aronian.
...but never again...unless of course a clear win position...

to save something else, or to prevent further harm?
Nice Q sacrifices shown in the several examples above.
I just wanted to add...
There is only one reason that I can think of for sacrificing the Q. And that is for strategic or tactical reasons leading directly toward killing the enemy's K.
Also, I think that some/many female players may want to stop thinking in terms of the Q being a woman. It is just a piece of wood or plastic. There really is no gender political correctness involved in the matter. In real life, sacrificing my queen is not an option.

your all thinking too much. the answer is YES. You will know when to sac her when you see the opportunity. do it for material, check mate, some kind of iminent positional advantage. look at the game of the century. I believe its fischer vs brown? you'll understand a lot after you see that game.
I just did. After a series of blunders by me in the beginning, followed by some better play culminating in opponent hanging his queen, we came to the following position. I decided my chances in endgame were much better, even with his rook, so I sacced my queen.
In the event the opponent blundered soon after and resigned, but it would have been interesting to play out the endgame.
Bxe5 does not deserve any question marks, it is the best move in the position. Your right it hardly affects blacks overwhelming advantage. White should've resigned many moves before.
I meant to put it by the move before Rxb1. However I don't think it's a ??, only a ? and perhaps a ?!

Everytime I hang my queen I call it a sacrifice. LOL
Ha - I like how you think. I'm going to start calling my blunders 'sacrifices' - maybe give my opponent a raised eyebrow a clever little smile to make him think I have something devious up my sleeve . . .
I don't think I've ever sacrificed my queen in a real game though - get plenty of practice doing it in tactical problems though!

Sacrificing a queen is a great tactical advantange, most players will focus on her, you can position and develop, then sacrifice, then win, if done correctly, that is.

Every game I start with Queen sacrifice, I almost try hard to sacrifice my queen within first three moves,if my opponent tries to stop i somehow try very hard to sacrifice it within first 10 moves.Once I have sacrificed my queen then I try to concentrate on checkmating my opponent.
but First priority even before checkmating your opponent or to save myself from checkmated is sacrifice my queen.
For couple of Sample examples.
http://www.chess.com/forum/view/chess-openings/a-very-detailed-queen-sacrifice-opening-ver-20
to save something else, or to prevent further harm?