The World's First Microprocessor (MP944) was a 20-bit parallel multi-processor (1968-1970 design by Ray Holt) running the real-time flight calculations (CADC) for the Navy F-14 Tomcat.

Back in civilian space, one year later in 1971 Intel would just be finishing it's first 4-bit commercial microprocessor, the Intel 4004, for use in a Busicom hand-held digital calculator...

Military chip designer Ray Holt went on to design the personal Jolt computer kits in 1975 using the MOS 6502 chip. This chip would subsequently be chosen by Apple, Atari, Commodore to power their 8-bit microcomputers see [3].

By the early 80s, the four big name 8-bit microprocessor chips were the Intel 8088 (in the IBM PC 5150) , Zilog Z80 (in the Amstrad and Sinclair), Motorola 6800 (not selected for designs because of price), and MOS 6502 (in Apple II, Atari, Commodore, and BBC/Acorn).

References
[1] US Navy F-14 Tomcat, MP944 processor and applications: http://firstmicroprocessor.com/

[2] Ray Holt and the Jolt computer, based on MOS 6502 8-bit microprocessor.
http://bugbookmuseum.blogspot.com/2014/10/vintage-computer-super-jolt-1975.html

[3] List of 80s computers and 8-bit microprocessors they used --
https://www.simplyeighties.com/80s-computers.php#.W3uh2roo_IU