I wouldn't know how to win it if the K+R player doesn't make a move that allows the Q a double attack on K and R. My best try for it is getting the Q close to the opponent's king, giving him checks and trying to limit his scope of movement so the opportunity for the double attack arises, but I don't know exactly how to force this.
K+Q vs K+R ends in Draw!

I hope this provides interesting discussion ... I see previous threads on the subject got nasty and ended. Let's load the intial position into our engines and let them fly. Can it be done in 50 moves? Might depend on the starting postion.

http://en.wikipedia.org/wiki/Pawnless_chess_endgame
In this 2001 game[1] between Boris Gelfand and Peter Svidler,[2] Black should win but the game was a draw because of the fifty-move rule
A queen wins against a lone rook, unless there is an immediate draw by stalemate or due to perpetual check

I hope this provides interesting discussion ... I see previous threads on the subject got nasty and ended. Let's load the intial position into our engines and let them fly. Can it be done in 50 moves? Might depend on the starting postion.
You don't need engines, the Nalimov base has all the answers:
http://www.k4it.de/index.php?topic=egtb&lang=en

Turns out David asked for a draw once he had a winning position. His opponent let him play on even though he brushed his king trying to move another piece. If he force him to move the king David would have drop a piece and lost. Mutual sportmanship and one for the history books.

i have studied a lot this endgame,its really fascinating,you have to learn some patterns,to triangulate and make the rook seperate from the king,the key is to make the king march to the third rank and simultaneously block the checks from the rook,so the key move in above potition is to play Qe4!!,not Qe5 that svidler played.
A game today at the world cup ended in a draw. I always thought is was a forced win when a good player has the lady.
Kevin