Many call the world's most popular free software-based operating system, "Linux," after the kernel it's built-upon, some call it, "GNU/Linux," but it should simply be called, "GNU."
The once common flame wars over what to call the world's most popular free OS have been reduced to dying embers, with most deciding to call the system, "Linux." This choice was shepherded along, in part, because of a desire on the part of corporations to distance the software they produce/support from the term "free" -- as in Free Software. (See About Free Software for more on that debate.)
Richard Stallman, the founder of the GNU Project and the Free Software Foundation, has long argued for the term "GNU/Linux", and many of his adherents use that label. Both groups are wrong.
The confusion comes from the legacy use of the term "operating system." Most texts on the subject have historically defined both the word "kernel" and the term "operating system" the same -- basically some version of: "the software that allows applications to communicate with hardware." For a while that definition served for both terms, but over time, due to sign slippage, the term "operating system" has evolved to mean something more like "operating environment," a larger more inclusive category that encompasses the kernel, user interfaces (shells and GUIs), software building/installation tools, as well as many other basic tools and utilities.
Referring to an operating system by the name of its kernel is very rare, in fact, it is much more common to do the opposite. Microsoft Windows NT, Unix, and the BSDs all name their kernels after the operating system (e.g. the FreeBSD kernel). Further, some operating systems have completely different names for their operating systems and kernels. Apple calls its operating system "Mac OS X" and its kernel "XNU" (which, in turn, is a modified version of the Mach microkernel).
Closer to home, for those of us who use Linux-based operating systems, Android OS is also built on top of the kernel, Linux, but no one insists on calling it, "Linux."
Be smart, be bold, be right: call it GNU.
