The recently released Top500 global supercomputers list shows that the free and open source operating system, Linux, has easily dominated the field and is indisputably the highest performance operating system on the planet.
Linux powers 95%+ of the super computers in the top 500 worldwide, and with China's recent launched Tianhe-2, the new king of the heap, the US loses its traditional lead in HPC (High Performance Computing). When Linux's share of the super computers is weighted by the actual computing power commanded (in FLOPs), it increases to 97.4% leaving all the other hopefuls in the realm of statistical noise.
In addition to its command of the highest end of computing in the world, Linux also owns the small end of the scale with marketshare leading Android smartphones, tablets, and other devices (Android is just Google's branded operating system built on the Linux kernel, and is also mostly open source). Between the higher and lower ends, Linux's pace of gradual domination is more leisurely, with traditional desktop adoption of Linux variants like Debian, Ubuntu, and Linux Mint on a very gradual incline, but the advent of simplified Linux variants like Google's Chrome OS which is based on the open source ChromiumOS project seems to be gaining substantial traction in traditional proprietary OS strongholds like schools.