It is not possible for a web host to offer 'unlimited' bandwidth or diskspace. But you can find lot of web hosting providers offering unlimited web space, bandwdith, etc... To provide unlimited web space, one need unlimited hard disk, bandwidth is costly.
Unlimited Web Hosting plans always come with clauses that restrict how much bandwidth you can transfer at a given moment, how much CPU usage you can use (which is arbitrarily decided), and so forth.
Can any Web Host offer unlimited bandwidth ? Yes, they can offer. But it cost unlimited. So everyone expect something return, that is unlimited return for unlimited web space and bandwidth. For example if a web hosting company provide free web hosting with standard banner on users web site can really offer unlimited web space and bandwidth if the users web site can provide unlimited banner impressions and not for creating a mirror of download.com or gnu.org