I believe we covered this somewhere else also but now we have a separate topic to deal with it.
Sometimes the websites themselves will tell you. They will have a mission statement or something similar.
However, those companies who also offer non-free products get their best advertising by word of mouth if people like their product. For instance... Lavasoft. They have a free version of their product that is available to people on an individual basis. Let's pretend you like it and it has saved you many times from spyware. The chances are that you're going to tell the IT department where you work how wonderful this software is and if they agree Lavasoft just profited from your company purchasing the commercial product for businesses.
Now on the other hand there is the belief that Free and open software makes for a better product. That is the reason why organizations like FSF (Free Software Foundation) exist. They believe that if someone codes a piece of software and make not only the program itself free to use but the original source code free to look at and modify; this will not only keep the programmers honest but it will also employ the talents of untold thousands of people who believe the same way. Maybe someone in Singapore is able to make the program work faster and reduce it's size. Well, everyone has just benefitted from this.
However, there are downsides to this also. Not everyone is willing to work for free or give out their ideas for free. But that is the very basic idea behind free software.
Here are a couple of websites that will give more detail concerning this.
http://www.fsf.org/
http://www.gnu.org/
http://www.opensource.org/
The next websites actually provide a place to look for and download free sortware. Chances are that if you're trying to do something. Someone else has thought about it also and made a piece of software to do it already. Not all these programs will be available for all operating systems but it is worth the look.
http://sourceforge.net/index.php (windows, linux, and pda)
http://freshmeat.net/ (linux only)