A mainframe, these days, is a large data-processing computer that mostly runs legacy applications. The dominant mainframe vendor in the US is IBM, and people often believe that IBM is the only one left. IBM's mainframes are the fastest, but not close to the only ones around. They have about 90% of the US mainframe market, but in other markets, half or less of mainframe sales are IBM. Some mainframe systems vendors focus on solid transaction-processing performance, while other vendors are mostly focusing on providing continuing support to legacy users without impressive performance increases. Combined, world mainframe sales are several billion dollars per year.
Unisys is the secondary player in the US market, and leads in market share in other areas, like Taiwan and Latin America. Formed in the 80's by the merger of two earlier companies, Sperry and Burroughs, Unisys has two operating systems: OS 2200 and MCP. OS 2200 is based on the UNIVAC Series 1100, a relatively late (early 1970's) system with a modern command-line interface vaguely reminiscent of VMS. It runs on the Clearpath Dorado line of 36-bit CISC machines. MCP is arguably the oldest operating system still in use, with its first version released in 1961. It runs on the Clearpath Libra, formerly called the Burroughs Large System, a strange 48-bit stack-based architecture. Unisys is one or the few mainframe vendors left that is actively seeking new customers and developing high-performance systems.
Fujitsu pulled out of the US and Japanese markets around 2000, having previously made IBM 390 clones running MVS. They're still active in the European market with the ICL VME and Fujitsu-Siemens BS2000 operating systems, both of which have been acquired from purchasing other companies. VME has substantial, although fading, market share in the UK. In the last few years, Fujitsu has been de-emphasizing it, putting OS development on the back burner and pushing a software emulator for Windows instead of delivering new hardware. BS2000, with a large customer base in Germany, still gets new hardware and OS releases, although Fujitsu is phasing out high-end 390-based processors in favor of commodity x86 chips running a mixture of ported and emulated software.
Groupe Bull, a French vendor, produces two distinct operating systems, confusingly called GCOS 7 and GCOS 8. GCOS 8 is the older of the two, originally developed at GE as GECOS and sold to Honeywell, who sold all their OS property to Bull in the late 80's. GCOS 7 is a more recent operating system, loosely derived by Multics and developed by Honeywell in the late 70's. Both systems are getting software and hardware refreshes, with the hardware based on off-the-shelf Itanium and x86 processors with custom firmware. GCOS is used heavily in France, although its market share is negligible pretty much everywhere else.
Hitachi develops two operating systems, VOS1 and VOS3, purely for the Japanese market. VOS3 is a direct clone of MVS, and runs on 390-compatible systems called the AP8800. VOS1 is being phased out, but before the hardware's unfortunate demise ran on a POWER-derived machine (probably a rebranded 595) called the AP7000.
NEC has several high-end in-house operating systems, including a high-end UNIX and the ACOS family, three GCOS-based mainframe operating systems. ACOS-6 was a rebranded GCOS 8, and has been end-of-lifed in the last couple of years. ACOS-2, the low-end system, was based on the long-dead GCOS 4 system by Bull; you can still buy ACOS-2, if you don't mind hardware running on Pentium III Xeons with a maximum of 256MB of RAM. ACOS-4, a GCOS 7 rebrand, is the only one still under meaningful development; it runs on reasonably fast Itanium hardware.
Is the mainframe dying? Maybe in a sense. NEC and Hitachi are probably going to pull out of the mainframe business in the next few years, perhaps followed by Fujitsu and Bull. Unisys and IBM will stick around for the simple reason that The Cloud makes the need for a huge, fast, hyper-reliable data-processing box more relevant, not less. IBM and Unisys have both had great sales numbers over the last couple of years, and I don't think that trend will stop any time soon. As long as mainframes stay fast and good at what they do, they can survive and thrive.