Some popular distributions of Linux that are completely free are Ubuntu, Fedora and OpenSUSE. Ubuntu is popular as a general use operating system and is very accessible for inexperienced users. It is polished and features one of the easiest installation mechanisms of all Linux distributions.
Fedora is the completely free version of Red Hat Enterprise Linux, a popular Linux distribution targeted at the commercial market. Red Hat Enterprise Linux is also available for free but has some support features that require purchase, as well as more restrictive licensing than Fedora.
OpenSUSE bills itself as the maker's choice for systems administrators, developers and desktop users. It is primarily targeted at more advanced users and features high levels of customization.