This page lists just a tiny number of the many astronomy software packages and new ones appear all the time. These are just suggestions and only scratch the surface. Each item has markers: F = freeware, W = Windows, M = Mackintosh OSX, L= Linux, H = html5, O = open source. In general, most astronomy software is written for Windows but Mac users may be aware that they can run Windows on their Mac by partitioning their hard drive (Bootcamp) or using a virtual machine (VM). A good free VM is Virtualbox and you can run Windows and Mac OSX simultaneously.
Stellarium http://www.stellarium.org/ F, W, M, L, O A realistic and straightforward planetarium program.
Celestia http://www.shatters.net/celestia/ F, W, M, L, O A simulator that enables the user to travel through space (and time) to planets and stars (using Hipparcos catalogue data). The program can be modified with 'add ons', see next item.
Celestia Motherlode http://www.celestiamotherlode.net/ F,O A frequently updated collection of extra objects and data that can be added to Celestia.
Registax http://www.astronomie.be/registax/ F, W A program that stacks frames from webcams, used with telescopes, and produces a final cleaner image. Very useful for planetary imaging. Note though that this software hasn't been updated recently and astronomers are moving on to Autostakkert. See below.
Autostakkert https://www.autostakkert.com F, W Considered a replacement for Registax. The website carries interesting information too. Autostakkert can run on Macs with a 'wine skin' available from the website (or use Bootcamp or a VM, see opening paragraph).
Starstax http://www.markus-enzweiler.de/software/software.html F, W, M, L Stacks multiple images taken by cameras with interval timers to produce star trail images. Very easy to use.
Pixinsight https://pixinsight.com/ W, M, L Powerful image processing software for astronomers but at a price and demanding a fast computer. The learning curve is also steep but the results are astonishing.
Universe Sandbox 2 http://universesandbox.com/ W, M, L A simulator that enables planets to be created, cratered, terraformed, destroyed, galaxies to be collided etc. There is free legacy version for Windows only. The latest version Universe Sandbox 2 (actually superscript 2) is still in development but can be purchased. It is apparently much more sophisticated than the legacy version.
Deep Sky Stacker http://deepskystacker.free.fr/english/index.html F, W For stacking images and associated operations. A wineskin version exists for Macs.
PhET (Physics Education Technology) https://phet.colorado.edu/en/ F, H Science simulations, including astronomy, from Colorado University. Some sims are now available in html5 and can be embedded in MARS webpages. Two examples are shown below and there is now a PhET page on this website.