Free software is the best type of software. Not free as in free beer, but free as in freedom. If you use free software, then you control your computer, but if you don't use free software then chances are that you don't control your computer. Richard Stallman, the founder of the GNU project (GNU is Not Unix) and the FSF (Free Software Foundation) makes plenty of excellent points in this video.
One of the greatest reasons to use free software over proprietary software is the lack of malicious features. The majority of free software does not harmful affect the user unlike proprietary software which can spy on the user, slow the user's computer down, or deny the user access to their own computer in some cases! In fact, the GNU project has an entire section of their website dedicated to the malicious features of proprietary software here.
You can find a countless amount of free programs in the FSF's free software directory here. There you can find a free program for any use. Need a free replacement for Microsoft Office? Use LibreOffice. Need a free web browser? Use Firefox. Need a free media player? Use VLC. There is a free program for every use and problem. If you need software for a very specific task, there's probably a free software solution.
If you want suggestions for very useful or very cool free programs, here are a few.