Rsyslog is packaged for all major distributions. Unfortunately, often rather old versions are provided. This is especially the case for so-called enterprise distributions.
As long as you do not run into trouble with one of these old versions, using the distribution-provided packages is easy and a good idea. If you need new features, better performance and sometimes even a fix for a bug that the distro did not backport, you can use alternative packages.
The rsyslog project offers current packages for a number of “big” distributions. They can be found at http://www.rsyslog.com in the download section.
Note that some distributions (like Fedora) usually keep up with development rather quickly and so we do not provide special packages for them.
Packaging is a community effort. If you would like to see support for an additional distribution and know how to build packages, please consider contributing to the project and joining the packaging team. Also, rsyslog’s presence on github also contains the sources for the currently maintained packages. They can be found at https://github.com/rsyslog.
If you do not find a suitable package for your distribution, there is no reason to panic. It is quite simple to install rsyslog from the source tarball, so you should consider that.