The MULTICS (Multiplexed Information and Computing Service) project was an attempt by MIT, General Electric, and Bell Labs to create a second-generation timesharing system based on MIT's CTSS. Eventually, Bell Labs dropped out of the project and this left one Bell Researcher, Ken Thompson with little to do. Finding a discarded PDP-7, he decided to write a smaller version of the MULTICS project in what was the customary systems development language at the time, ASM. Thomposon's project earned the name UNICS (Uniplexed Information and Computing Service) from Brian Kernighan as a joke on MULTICS but it stuck and eventually became..Unix.
His collegues were quite impressed with his effort and soon after, Dennis Ritchie joined Thompson and decided to move Unix to the more modern PDP-11/20 which would greatly help its later success. To do this, Richie and Thompson rewrote the whole system in a new language created by Richie, C. Then in 1974 Richie and Thompson wrote their landmark paper about Unix recieving the ACM Turing Award for their efforts. This event only helped stir interest in Unix and soon universities (Most happened to use the PDP-11/20s) from around the United States were requesting copy's of the Unix source code from AT&T. Since AT&T was forbidden by the government to enter the computer market, they willingly gave out the source for a modest licensing fee.
Eventually Version 6 came around and was replaced by Version 7 (Microsoft's Xenix was based on it), the first truly portable version of Unix. However, it was during the time of Version 6 that the one of the most significant changes in Unix history would occur. The University of California Berkeley had acquired the Unix code and modified the code significantly as well as adding many utilities such as vi, csh and Pascal and Lisp compilers creating the BSD distro. Berkeley Unix was well funded by ARPA and other government grants and as such was chosen to create the Internet protocols of today (TCP/IP).
By the 3BSD release the Computer Science Research Group (CSRG) lead by Marshall Kirk McKusick at Berkeley had managed to port it to the VAX and eventually the last relelase 4.4BSD before they dissolved in 1992.
This would prove to split the Unix community in 1/2 with some adhering to AT&T's "System V" standard and other to BSD's standards. This was resolved with the creation of POSIX to make all Unix systems compatable with each other by creating a standard that all Unix variants must comply with.
Today, Unix runs most of the world's most powerful servers and has become a multimillion dollar industry. All built on the side project of Ken Thompson.
BSD Unix Variants
System V Variants
Those italicized represent Unices that share ample code from each type of Unix.