Website for Students to Upload Homework

I don't want students to e-mail their assignments, so I'm looking for a site that allows me to not only post homework and share handouts, but also for students to submit/upload files. In the past I've used Edline and Turnitin, which my former school has accounts with; but the disadvantage to this arrangement is I lose access to my lessons and calendar when I leave school. So now I'm trying Google Sites and wikis like Wikispaces and Wetpaint. But I'm still not sure if I really want students to have editing access to other pages and their classmates' work. I just want them to be able to upload documents and photos to specific web pages. Any suggestions?