Why do you think UNIX has lasted so long and not been completely replaced?
You could almost answer this with one word. "Stability"
Telcom's all over the world rely heavily on Unix as they are expected to achieve far greater than the five 9's.
Unix is the father of open source. If it does not do what you want, you can alter or add your own code to it. As a result, I believe there are over 200 Unix variants to date.
Of all the operating systems, Unix has the least number of remote root compromises. That is huge!
I wonder how long the Internet would be useful if the root DNS servers were running Windows Server 2003? The Internet would probably be brought to its knees in less than 5 minutes. Thank God they run Unix!
At its core, Unix is still the best at crunching large amounts of calculations. Many banking systems still rely heavily on a variant of Unix.
Mac OS X is on the rise. Under the hood, OS X is Unix. Thanks to the IPod, Apple is selling more Mac's than ever. Who would have thought a device like an IPod could put Unix into millions of homes.
Unix is so portable. Billions of people use Unix everyday and are not even aware of it. ATM machines don't tie into a windows box. Most use a Unix server or Mainframe as a back end.
Lastly, did I mention that Unix is stable?