Dreamhost does this regularly, and you can find more information about it in the Dreamhost Wki article on .snapshot directories, and other pages linked from there regarding backups at Dreamhost. The “.snapshots” are a great feature, and can often be used to “recover” if you seriously “bork” something.
That said, you should never rely exclusively on a third-party host, no matter how “solid” they are for an important backup. That is your responsibility, and do abdicate that responsibility to another is neither professional or realistic and can lead to you experiencing a major disappointment.
Even if the backups are flawlessly maintained by Dreamhost, if some major disaster were to knock them completely off the net for an extended period of time, your inability to get to those backups would make it hard for you to resurrect your site on another host.