Really free? Yes! I have used both Starry Night and Red Shift and they are good products. But right now I’m doing fine with free alternatives. Here’s some great free astronomy software:
1. Stellarium – Your desktop planetarium. It will show you the sky in 3D. It’s a great first planetarium, well made, very easy to use and good looking. To be fair, it’s not the best and it doesn’t have all the features you might need later on. Still, it’s a software you’ll keep installed on your computer. This software works on Mac & Windows.
2. Google Earth – Very useful in itself, but from version 4.2 it also has Google Sky included. Maybe you already have it? There’s probably no limit to what information you can add and display in Google Earth. Among all that information I think NASA’s Earth at Night layer is the most useful for the night sky observer.
You’ll find the layer in the Gallery. Look under “Featured content. This is a great tool to help you find a dark place for observing the stars.
A very fun addition in version 5 is Google Mars. While on Mars, fire up the built in flight simulator and take a tour through Valles Marineris. This software works on Mac & Windows.
3. DarkAdapted – When you’re out there at your dark place with you binocular or telescope you may want to bring your laptop. The problem is that your screen is to bright, it will ruin your night vision. One solution is to cover the screen with red transparent film since red light is better for your ability to see in the dark. Or you use software to change the light from you screen. DarkAdapted is such software. Some software, like Stellarium, also have functions like this. This software works on Mac & Windows.
4. BOINC – Help SETI@Home to find E.T. What most people consider is just for fun could be the biggest discovery in the history of mankind. And with this software it can be you who identifies the signal. You can use BOINC in other areas too, like medicine and mathematics. All work is done with processor power you don’t use. And yes, it works on both Mac & Windows.
There are of course other freeware you can run on your computer. All the above are easy to use, works on both Mac and Windows and are of course free. There is one more I’d like to add to the list, but there is no Mac version for it 
It’s called Virtual Moon Atlas and it’s the only software I miss after I left the Windows world. Very useful when observing the Moon!
When it comes to desktop planetariums, I must mention Sky Charts and C2A. Sky Charts, aka Cartes du Ciel, is probably the most used astronomy freeware in the world. There are versions for Windows, Linux and Mac OS X. Like C2A I’m not using it so to be fair I’ll not try to review it here.
For mobile users there is a java application, Mobile StarChart, for java enabled phones. It doesn’t work on all java phones but tested OK on my Nokia N95.
Edit: Virtual Moon Atlas IS available for Mac!
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