The big irons including IBM S39, Sun high-end servers, and some others. I have no idea if Unisys or any of those other Seven Dwarves are still in business.
There are expressedly built ones such as Deep Blue the chess playing computer, and ANSI (?) White for simulating nulcear explosions.
For the historians out there, be sure to check out Old-Computers.com for a walk down memory lane.
Be, (can’t find their homepage), before they started porting BeOS to hardware platforms, actually made their own computers, too. This article on Blinkenlights mentions them briefly.
Yup, the Amiga still seems to be chugging along. For latest products see below.
BAND NAME!
Although people occasionally mention CISC versus RISC in these discussions, it’s really an ancient (in computer terms) argument. Back in the '80s there were systems that could really be called RISC systems, but they started borrowing from each other and the distinctions blurred in early the '90s and went away by the late '90s. Most modern processors have a mix of what would have been CISC and RISC in the old days, and have architectural changes like the ability to execute multiple instructions at once that blur the old distinctions.
Anyway, the original question is somewhat vague - what do you mean by a ‘different computer’? Do you mean a completely different processor, or would the same processor but with different supporting hardware qualify? Also, modern macs don’t use a descendant of the old Motorola processors - they use the PowerPC chip made primarily by IBM.
Anyway, some of the common systems are here:
(Note that these all use different processors from Apple/Intel, except for the RS/6000).
Sparc by Sun (Used as high-end workstations and as servers, usually run Solaris)
RS/6000 by IBM (Used as high-end workstations and as servers, usually run AIX)
PA-RISC by HP (Used as high-end workstations and as servers, usually run HPUX)
These are all pretty common in various business uses and are something you might be near the actual box for typical use. There are a lot more workstation type machines (SGI, Alpha, and others), each with distinct processors.
There are also mainframes that typically sit in a back room (and take up a few closets worth of space, though in the old days they’d take up a warehouse and a staff), IBM is the big producer and each of them use their own hardware which is very different from PC hardware. These systems are built for serious reliability, as in not being shut down for a decade at a time. The AS/400 (also by IBM) is sort of a baby mainframe, it’s relatively small, cheaper than the big iron, and does similar tasks.
There are also supercomputers, which are used for really massive number crunching (though they’re generally not as good at handling huge databases as mainframes). Some of them use their own specially made processors, but a number of them make use of huge numbers of regular processors (Intel made one with something like 500 Pentium Pros a while back, for example).
Then there are also embedded processors, the little chips that get incorporated into things that have a computer but no normal interfaces, like clocks, cars, industrial robots, and anything else that has computer control. In many cases these are specialized chips, but for some applications older processors like those in Apple/Intel machines get used.
And this trend is continuing. The IBM Blue Gene currently being developed will have over a million processors.