UNIX may seem like something that's far, away, and old, but the fact is that UNIX is still going strong today, with its influence visible everywhere in the world of computing. While Windows may not be UNIX-based, its two biggest competitors - Mac OS X and Linux - decidedly are. With Linux and Mac OS X gaining in popularity all the time, you could even say that UNIX is making a comeback (assuming it was ever gone).
The move away from UNIX to Linux, a move that is gaining in popularity, is often seen as a nail in the coffin of UNIX, but I tend to disagree with that notion. I don't see "moving to Linux" as "moving away from UNIX", but more as moving on to the next level of UNIX; an open UNIX, a Free UNIX.
Looking at the origins of UNIX, you could even go as far as to say that Linux more closely aligns with the original goals of the UNIX creators than UNIX itself does now. Ken Thompson and Dennis Ritchie had the following to say about the goals of UNIX:
Now let me ask you: which aligns better with these goals, Linux or UNIX-proper?