OPENSTEP 4.2 for Mach is the last incarnation of NeXT's OS to be actually sold by NeXT, or to run on their hardware. It was succeeded by Rhapsody and later Mac OS X, and descended directly from NeXTSTEP. Its interface is virtually identical to that of NeXTSTEP 3.3, featuring the global menus, Workspace Manager and Dock that made it so iconic. Unfortunately, the revamped user interface seen in the NeXTSTEP 4.0 developer betas, featuring a shade button, gradient-filled titlebars, flat window decorations and a tabbed shelf did not make it into OPENSTEP, and appears to be lost in the mists of time. The major difference between NeXTSTEP 3.3 and OPENSTEP is in the API, which has been standardized to the OpenStep (note the capitalization difference) specification. It will therefore run most NeXTSTEP applications, but also supports a new, superior API that its predecessor did not have. Also, significantly, OPENSTEP dropped support for the various HP PA-RISC workstations, though support for the Sun SPARCstations remained. NeXT intended to port the OS to the Motorola 88000 and PowerPC, and possibly also to the DEC Alpha and Sun UltraSPARC, but NeXT folded before this could happen.
Any Motorola 68040-based NeXT. The original MC68030 Cubes are officially not supported, though many sources state that it does indeed work, albeit slowly. This is the original platform, and obviously, all hardware is fully supported.
Sun SPARC hardware
The only machines officially supported are the sun4m series, though there are sporadic reports of people convincing OPENSTEP to run on sun4c systems. In either case, the only supported processors are the SuperSPARC and MicroSPARC series. The Ross HyperSPARC and Texas Instruments TurboSPARC processors aren't supported at all, and the kernel will choke and refuse to boot. It's also rather picky about graphics devices - the only framebuffers that work are the BW2 (monochrome), CG6/GX (8-bit color, accelerated), CG14/SX (24-bit color, accelerated, SPARCstation 20 and rare SPARCstation 10s only), and the TCX (8-bit or 24-bit color, accelerated, AFX bus). This last one is hard to find, and works only on the SPARCstation 4 and SPARCstation 5.
Other hardware, such as ethernet, sound and SCSI, along with the standard Sun serial and parallel ports work. The SPARCstation 10's onboard ISDN does not, however. (It works only with Solaris).
Hardware support on x86 is a can of worms. There are fairly few hardware drivers available, but a surprising amount of modern hardware can be convinced to work. In any case, you'll need an 80486 or later CPU, the 386 won't cut it. You'll also need some sort of supported mass storage controller - IDE works, as do a fair few SCSI cards, but Fibre Channel is right out. Graphics is a challenge, too, but a good general rule is that cards which work under OS/2 work under OPENSTEP. Later patches also add a VESA graphics driver which allows nearly any card to work, at least somewhat. Sound and ethernet are challenges too.
All that said, OPENSTEP will run on some surprisingly modern systems, and is quite performant relative to NeXT or Sun hardware.