Webhosting Terms and Definitions
Webspace (or "web space") refers to data storage space accessed via the Internet, usually used to host websites and data files. "Unlimited webspace" (or "unlimited web space") means just that, no limits, and therefore is impossible -- all hard drives have a maximum amount of file storage space. Unfortanately many web hosts claim to offer this, although it is often qualified in their terms of service (TOS) to be less. What the hosts mean is they have no set limits for users' allowed file space other than those caused by their own webserver's limitations.
Here is a list of free webspace hosting companies claiming to offer Unlimited Webspace.
Free Web Hosting