I'll be the odd one. I like everyone to have their own case and be in charge of their own stuff so we do 4 people/4cases. When we're on an airline that charges, we all do carry-on size. Each person also does their own personal item- DH likes a backpack, DS always preferred a messenger bag, when DD was little (3,4,5,6), I had her use a backpack so that she could wear it, and now DD and I both like a larger (usually Vera) bag. Whenever possible, we fly Southwest and then DD will pack a larger case and check it.
My DS is grown and my DD just turned 16 but I did one case per person from the time they were little. When DD was too small to pull her own, DH could easily manage 2 small cases. By 5 or 6, she could easily pull her own carry-on size. My kids started helping me pack their stuff early on and by 10 or 11 could pack their own with supervision. DS needed supervision to bring enough and DD needed help editing. Once we were on the trip, it just seemed like everything was more organized and easier for everyone to get ready if people's stuff wasn't mixed together.
We're not big souvineer shoppers but on last year's Disney trip my DH and DS had plenty of room in their cases for the stuff we bought and everyone always has room in their personal item/backpack.
One more thing, when my kids were in the 3-maybe 6 age range, I would let them choose outfits and then we would pack each outfit together and then once on vacation they could pull out an outfit and dress themselves. Very quick and easy.