No one actually owns the Internet, and no single person or organization controls the Internet in its entirety. More of a concept than an actual tangible entity, the Internet relies on a physical infrastructure that connects networks to other networks. There are many organizations, corporations, governments, schools, private citizens and service providers that all own pieces of the infrastructure, but there is no one body that owns it all. There are, however, organizations that oversee and standardize what happens on the Internet and assign IP addresses and domain names, such as the National Science Foundation, the Internet Engineering Task Force, ICANN, InterNIC and the Internet Architecture Board.
Also see the A Brief Timeline of the Internet in the Quick Reference section of Webopedia.