One thing I wish Mozy (or any other backup company) did was allow the user to prioritize their backups. For example, I’d want my documents backed up first, then my photos, and finally my music. The initial backup should go in that order; if something in my documents is changed before my music is backed up, the updated document should be backed-up, before the music upload continues.

IBackup has an option where, if you’re backing up more than 100GB, they’ll ship you a drive where you’ll do your initial backup to, then you ship it back to them. Something like that may be a logistical nightmare for a company like Mozy (with all their Home users), but for IBackup (geared more towards businesses) it seems to work.
http://www.ibackup.com/online-backup-faq/faqq96.htm#8