At our house we call Saturday "chore day." On Saturday, besides cleaning their bedrooms and making their beds, our kids are also assigned a few extra jobs to help our house stay semi-tidy and help things run smoothly.
As part of "chore day" everyone has to empty his or her bedroom garbage can, vacuum the bedroom floor and put away his or her laundry. Since the garbage and laundry and floor mess belong to the children we feel like it is their responsibility to take care of those and we don't feel one bit ogre-ish having them take care of those chores.
But on top of those simple once a week tasks each child is assigned a couple of additional jobs (yup, we're slave drivers over here). These jobs are usually things that aren't that hard, but help maintain our house and keep it resembling a dirt free zone (ha ha, at least that's the idea).
Anyway, the point is a few weeks ago I decided to make a "chore day" chore chart so the kids didn't have to follow me around in the morning asking for the easiest jobs and so I no longer have to think on my feet what things to have each child do. This alternating wheel of household assignments has been a fabulous addition to our family. I love that no one fights over jobs anymore (you know you're in trouble when kids are fighting over which chores they want to do). I love that things are more organized (I really am a type A personality at heart, although you probably wouldn't know it anymore).
This chart has worked wonders for us, and maybe it will help you out as well. What ideas do you have to keep your kids from fighting about the things you ask them to do? I'd love to hear your thoughts or what works in your house.