Great question. I've been giving this some thought as well. This is not exactly the information you asked for, but rather some negotiating advice: In general, when you ask for a discount offer something in return--even if it's not significant. You will feel better about it and it gives people more dignity. That makes it makes it easier for them to both accomodate you and easier to say "No" without being awkward. Also, it opens the door to counter-offer with terms that really do work for them.
Specifically, how to apply that to Europe is to say "I am on a budget, do you offer....blank...."
Then find an appropriate offer such as: "Do you offer a cash discount?" "Do you have an off-season discount for April?" (If it's their busy season they'll tell you.) "Can I get a discount if I get the room without breakfast?" (Maybe they would be happy to sleep in...) "Do you offer a discount if I stay for four nights?" "Do you have a less expensive room, perhaps one without a view?"
I too feel uncomfortable asking for discounts, but if you do so respectfully I'm sure they won't offer a deal they can't afford. If they really want to fill the room, they'll make you a deal and everyone is happy.