the smart ass in me wants to say... yeah but you will need an unlimited hard drive and an unlimited backup software.
the nice person in me wants to say..... you will have physical limits somewhere the size of the drive,
the amount of data being stored (how much of this actually changes?),
you will need to find a limit and work from that (your very unlikely to get an unlimited backup provider, although there are ones that offer unlimited amounts of space but charge you per GB for what you use)
what operating system are you using? windows,linux?
what type of access do you have? is the server yours or are you on a reseller plan?
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well your question is vague, but its a yes and no question, yes its possible to have unlimited hard drive, through cloud/clustering systems, like amazon s3, were you can use as much as you want, but you'll have to pay for usage, the same goes for bandwidth, if you have dedicated line, you can use unlimited to the limit of the line, so you can achieve unlimited resources, in some ways, but if you are talking about a single server or shared account, that is not possible, since the resources have a physical limit.
^_^.oO( im in hostcult.com huhumm i'm also hosted by: servint, jaguarpc and dreamhost its all good hehehe )
This is a tricky job and an important one..
What you can do is, you can purchase Regular Backups at webhosts like JustHost, Ipage etc..
The people out there will do this job for you and obviously, they'll be responsible for this.
You just need to make sure your site backups are being made or not.