Look into an Amazon S3 web services account.
They offer several different 'grades' of storage and on different continents at different prices.
Amazon S3 is incorporated into many website gallery and other modules which generate a lot of storage requirements, which are of course expensive on a dedicated or purpose specific server, and using your sites servers for such things don't make a lot of sense.
I use them for both my site (galleries, blogs, etc are actually located on Amazon S3 but this is transparent to the user), and personal backup. They don't cap their speeds.. so if you have a 50mbps connection you can go both ways at 50mbps. You can choose from several different levels of encryption, or none at all. All my personal files are encrypted, but my website load I don't bother to.
Very cost effective.
Rackspace Cloud Storage is also something to consider.. also becoming popular with web professionals.. though they have a different pricing structure which may or may not suit your needs.