The Intel 8008 CPU was the world's first microprocessor; it was an 8-bit unit. The first chips were made in 1971 and announced in March or April 1972. It had a clock frequency of 0.5MHz, or 0.8MHz for the 8008-1 variant pictured to the right. The 0.8MHz variant was available as early as June 1972.
The 8008 was commissioned by the Computer Terminal Corporation for their ground-breaking Datapoint 2200 programmable terminal product; the instruction set was designed by CTC, not Intel. Due in part to issues at Intel, the chip was delayed, and when it did finally appear, it did not reach the performance CTC had specified; so CTC wound up using a CPU of their own design, implemented in discrete TTL logic, in the 2200.
The design of the 8008 actually started only slightly after the preliminary thinking about the 4004 (the first microprocessor actually sold) but was put on hold (partly because CTC, which was funding the development, ran into business difficulties), and re-started after the 4004 was finished. This is reflected in the original naming used for them, which was '1201' for the 8008 and '1202' for the 4004: '1': P-MOS, '2': Random logic, '01': Serial number ('02' for the 4004). Both processors were renamed for marketing reasons. 
- http://www.youtube.com/watch?v=GG6goCIWCYY (Craig Solomonson's 1972 Intel Microcomputer)
- http://www.righto.com/2015/05/the-texas-instruments-tmx-1795-first.html (Ken Shirriff's article about the first microprocessors)