All of DreamHost's data is backed up, but generally only for in case of hardware failure. Your home directory is also backed up in a local .snapshot directory in case you goof something up.
That said, real backups are your responsibility. The nice thing about IMAP is that you already have a local backup, which is your mail software.
IMAP has a feature to Sync mailboxes. If the server loses its data, you can re-sync and your local data will go back up to the server. This is also handy if you want to transfer your IMAP mail to another account.
Since I regularly back up my home computer, I'm all set in case of any disaster.