Hi Niels,
I've done this through custom code making sure that a folder for the logged in user exists underneath a "Users" parent folder, which lives underneath a "Files" folder which lives in the "web" folder.
Then everything for that user is stored in and below that particular user folder, unique for that user (logged in).
You can do this with code on the login, a global variable or two (for holding base paths), and then code whereever you need to store files that are uploaded or accessed, that retrieves from the unique path for the user (that can be set in the session on login).
Stu