Yours is a list of free TeX distributions.
The better maintained TeX distribution, with tens of developers. The distribution of choice on all operating systems. Some GNU/Linux distributions provide it in their packaging framework (Debian, Fedora, OpenSUSE,…), but these prepackaged versions usually lag behind the basic one.
2. teTeX
A defunct TeX distribution once maintained by Thomas Esser, for Unix systems. Perhaps the first TeX distribution in modern terms. It was based on Web2C like TeX Live, and provided some tar archives to just download and install. On some flavors of Unix one needed to compile the binaries, though.
3. fpTeX
A defunct TeX distribution for Windows.
4. emTeX
A defunct TeX distribution for MS-DOS and OS/2.
A TeX distribution for Windows actively maintained by Christian Schenk. Many Windows users prefer it to TeX Live for ease of installation because it is based on a Windows Wizard. Recently it has also been ported to Linux and macOS.
6. proTeXt
A TeX distribution for Windows, essentially MiKTeX with something added.
Essentially the same as TeX Live, but only for Mac OS X. It adds some features to TeX Live for better compatibility with the OS.
8. gwTeX
A defunct TeX distribution for Mac OS X once maintained by Gerben Wierda.
9. OzTeX
A TeX distribution for Mac OS up to version 9 (but still runs on some older versions of Mac OS X). The first free distribution for the Macintosh. Not based on Web2C, the source were translated from WEB Pascal into Modula-2.
10. AmigaTeX and PasTeX
TeX distributions for the Amiga.
What are the differences? Well, disregarding the defunct ones or those that run on obsolete operating systems, there's not much to say. For Unix systems there's essentially only TeX Live.
For Windows one can choose between TeX Live and MiKTeX. The binaries of the latter have some different options from the former; which one to install is essentially a matter of personal preference. Both are based on Web2C.
Best Answer
No, TeX distributions don't cease to work.
Yes, LaTeX used to have a protection mechanism for suggesting users to update their LaTeX kernel. In the first years after the release of LaTeX2e, yearly updates were issued and there was a check whether the kernel is older than five years.
Such a check is performed only at format creation and it's sufficient to go past the error message hitting return in order that the format is created anyway. The check has been disabled with the 2010 maintenance release, IIRC.
However, a TeX distribution that contains a five year old LaTeX kernel is irremediably outdated and should be updated.
Here's the relevant code from
ltvers.dtx
:In a very old LaTeX kernel I found on my disk (2001/06/01), the check was inactive (but had 30 months instead of 65). From the change annotations we can deduce that in 2004 the bonus period was raised from two to five years, but at the end of these five years the kernel was considered sufficiently stable to allow for disabling the check again.
Thus only kernels dated before 2009/09/24 are affected. But, as I said before, having a kernel dated before 2007/06/30 means that the LaTeX system distributed with it is really outdated.
As Joseph Wright comments there is no magic trick for avoiding the check during format compilation other than acting on the computer's clock, changing the year to 2009 before starting format compilation; then the clock can be reset to the current date.