Unix was originally a product, first developed in AT&T's Bell Labs. But today, the word “Unix”, except in historical context, means a family of operating systems, not a single product (similarly to “Linux” meaning a family of distributions, not a single product). This family has a somewhat complex history (see also Evolution of Operating systems from Unix).
It's difficult to say when this product ended, because the original code was licensed to a number of vendors, some of which still maintain their product. I believe the last product released by AT&T was Unix Time-Sharing System 10 in 1989. However by that time most Unix systems were actually modified versions of the AT&T code maintained by other companies such as Sun (SunOS, later renamed Solaris), Hewlett-Packard (HP-UX), IBM (AIX), etc. These three are still extant today, and they're directly derived from the AT&T code (although after over 25 years there probably isn't much of the AT&T era code remaining).
In addition to unix systems that are derived from the AT&T code, there are systems that don't contain any AT&T code but have a similar design and compatible user and programmer interfaces. The main families of such unix systems are BSD (FreeBSD, OpenBSD, NetBSD, Darwin/macOS etc.), Linux (many distributions) and MINIX.
Just to add to the confusion, UNIXⓇ is a trademark (actually, a family of trademarks: there are several versions) which does not designate a particular product: any product can use it as long as it passes a series of conformance tests. This unusual situation is a consequence of a long legal battle. Basically, a product can lay claim to one of the UNIX trademarks if it complies with the Single UNIX Specification, which describes user and programmer interfaces of the operating system (but not administration interfaces).
If you want to run a product that came directly from AT&T, you can run Unix V5, V6 or V7 on a PDP-11 simulator (the PDP-11 was a popular series of minicomputers in from the early 1970s to the early 1990s).
If you want to run a product based on code from AT&T, you can run OpenIndiana, which is based on the now-discontinued open source edition of Solaris (OpenSolaris). OpenIndiana is free software and runs on a PC. (It might not support as much hardware as Linux does though, but it can run in e.g. VirtualBox.) I believe that you can also download Oracle's Solaris for free for personal use, and it too can run on a PC. As far as I know, it isn't possible to run AIX or HP-UX on easily-available hardware or emulators.
If you want to run a product which has the UNIX brand, you can go through the official list. It includes several versions of Solaris (including PC versions), several versions of macOS, and a few uncommon Linux distributions. In a twist of fate none of the historical Unix products have the UNIX trademark, because they're too old and fail to meet some of the newer requirements for the UNIX brand.
If you want to run a product in the unix family of operating systems, Linux is one (or rather Linux is a subfamily, and each distribution is a Unix-like operating system).