The stackable plastic crates/boxes that i have from Ikea have lids but they rest on top as opposed to snapping shut tightly. You can just move the lid off really easily. The also have an insert with a handle for being extra tidy and sorting things. DS1 is quite tidy and like his things fairly well laid out. (Wonder who he gets that from?)
But at least having a lid means they are all stackable and they are clear so the kids know what's in each one (blocks, playdough, trains, paper, junk!).