The achievement of laundry depends upon WHEN you want it accomplished. When I asked this exact same question of our homeschool group (72 families), these are the leading answers I received:
1). WEEKLY - All dirty laundry gets sorted (e.g. - whites vs. darks) into the appropriate laundry cart or receptacle as it is discarded by the user, so it is ready to toss in the Magical Washing Machine on Laundry Day. The loads then are run endlessly in the background on Laundry Day, say Wednesday (or whichever day), every week by whomever is available at that moment or a different assigned kid each week. (Hint: Use timers so you don't loose track of loads being accomplished!) Then, the NEXT day, the entire family gathers for one hour in the family room, the parents' bedroom, or wherever to dump ALL the clean laundry, sort, fold, and put it all away. Voila!
BENEFIT: "Laundry doesn't rule our lives. Every. Single. Day. It's only once a week and we actually talk and laugh a lot doing it together."
2). DAILY - All dirty laundry (regardless of color .... let's be honest, it IS just mostly kid clothes) gets tossed directly into The Magical Washing Machine at bedtime at night. In the morning, the washer and dryer are run by an assigned kid per day before and after breakfast. After school, the assigned kid removes, sorts, folds, and puts away everyone's laundry. Since this is done daily, it's only just one load. (You also could have each person retrieve his or her own folded laundry and put it away.)
BENEFIT: "Laundry doesn't become a huge, looming 'To Do' mountain. Once the kids get used to this pattern, it really is a quick and easy task. The littlest ones apprentice and 'help' whichever older kid has been assigned to the task that day."
3). LAUNDRY NIRVANA - Each child is assigned a day that is his or her Laundry Day. That is the day on which s/he has the machines completely to his or herself to launder clothing. If you snooze, you lose. Feel free to barter with your siblings. (This mom had seven kids, so each kid had the same day each week. She also didn't implement this with each kid until the child reached second grade, so she still had the littlest ones help her do theirs.)
BENEFIT: "The kids are doing their own laundry! Helloooo!? Ta-da!!!"