Originally, there were Lattice C (the big gun), Wizard, Datalight, Ecosoft, DeSmet, Mix, Whitesmiths, BDS C, Manx Aztec C, and another one or two whose names escape me.
Lattice sold their compiler to Microsoft who relabelled it as their own for a while. If memory serves, MSC 4.0 was the first real Microsoft C compiler. Lattice continued (through version 6.2?) and was bought out by SAS, who dropped out of the DOS market.
Mix sold CP/M compilers and moved to DOS with their Power C, which they still sell.
Ecosft, BDS, and (I believe) Whitesmiths are history.
DeSmet lives on in the PCC shareware compiler although it's never been upgraded from its pre-ANSI beginnings.
Manx continued to make their Aztec C for a variety of platforms (I have their C65 for the Apple II), up to including PC's and Mac's. As their market share dropped, they tried to make the move to specializing in embedded systems development, but it was too late. They disappeared a few years back following the loss of market presence of some of their target platfoms (various 6502 machines, Atari and Amiga 68xxx, etc.)
Datalight C became Datalight Optimum-C (the first PC C compiler with a real optimizer) which became Zortech C++ which became Symantec C++. Merged to some degree with Think C, it continues.
Wizard C was bought by Borland after their own aborted attempt to produce a compiler in-house. It begat the entire line of Turbo C compilers. Turbo C++ was pretty much a rewrite which has since begat the rest of the Borland line.
Borland's original C compiler was only ever distributed in CP/M format. It was sold to Top Speed and became Top Speed C. A later rewrite turned it into Top Speed C++ before the company was sold to Clarion. I don't know the current status of that product.
Bob Stout