L.T.
I know how you feel. That whining really gets under my skin. My 3 yo has finally stopped whining (mostly) but now my 2 yo has begun. I do the same as the other moms have posted. I tell my kids I don't understand what they are saying and I can't help them until they speak clearly in a big boy or big girl voice. Then I go about my business and don't give them too much attention until they talk without whining. I smile and use a happy voice when I tell them how nice it is to be able to understand them and help them.
If they were whining about something they aren't allowed to have or do I then use a time out type approach. I might put them in their rooms and let them know they can come out when they are finished. Sometimes I remove myself from the room (or go to a different area of the room) and tell the kids I'll come back when they are done whining.