It does not look as easy as Dropbox (because there is a distinction between the JungleDisk software and the underlying storage), but it is not difficult either. I have been using it a little while and like it so far.
There is also no iPhone or Android app, but there is a pretty decent web interface.
Not the case any longer, iPhone app is available (I haven't used it yet): https://www.jungledisk.com/iphone_app_backup_share_files_man...
I'm sure an Android version is in the works.