We play a game called, "You make the mess, you clean it up." This is awesome because EVERYONE (parents included) is in charge of cleaning up after themselves. It makes so much less work for the parents.
Example from today: DD2 had eaten lunch and wanted to go play.
Me: Did you bring your dishes over?
Me: Did you put them in the Dishwasher?
DD: No, but it won't be that much more for dad to do tonight.
Me: Is it your mess?
DD: Yes (with a bit of a whine mixed in)
Me: Then who should clean it up?
That was the end of the conversation. She went back and put her dishes in the dishwasher.
Now there are many times where we have to help each other. For this I hear, "But that's not my mess!!" True, but we are in a family and there are times we need to help each other. During one of these comebacks from the kids, I remind them of a time where that particular family member helped them. If that doesn't work, then I threaten to stop helping them in some way like cooking their dinner, paying for lessons, or driving them somewhere. That stops the whine sessions pretty fast.