The most common weekly chore is cleaning up all the crayons and paper clippings that fall to the floor under their art table (aka our formal dining room!). They make the mess, so they should clean it. But in the end, we're working as a team because I immediately vacuum. So in a way, the chore is less a chore and more a family activity - albeit not the most exciting one! My oldest (6) also folds and puts away her weekly laundry. I'm happy to wash her clothes, so long as we work as a team and she puts them away.
Dusting and laundry, in addition to picking up their mess and cleaning their rooms, are the two biggies. They also help out as needed with dishes, setting the table, preparing dinner, and other tasks that must be done for the benefit of the family. We can't wait until they are old enough to shovel snow! :)
My kids have weekly chores of making their bed, clearing their plates at mealtime AND pushing in their chair (pet peeve of mine) and picking up toys. My boys, who are 9 and 7, also have to take out the trash, vacuum and dust, plus help dad in the yard. So far so good, but my husband tells me they should be doing more.