Yes. Some email provider offer unlimited space. But I guess you have to transform your files to bit and email it to yourself by 10000000000 emails.

They've done this before: http://en.wikipedia.org/wiki/GmailFS

Access time would be atrocious though I'd imagine. That's how you do 'unlimited space' when the space is your product (as opposed to someone selling someone else some space). Load servers up to the gills with 2/3TB drives then pepper it with all these emails. Some will even show you what sort of minimum budget you'd require: http://blog.backblaze.com/2009/09/01/petabytes-on-a-budget-how-to-build-cheap-cloud-storage/

Stu