Most folks reading that question would probably answer, “sure, but it would sound so terrible that it wouldn’t be worth it.”  Free music recording software?  Really?  Read on intrepid budding recordists!
If you want to start recording audio, you can definitely do that from home.  You probably already knew that.  But did you know you probably already have a home recording studio?  No, really!  If you have a computer with a sound card, access to the internet, and a PC microphone (even one of those cheap plastic ones!), you are ready to rock!  Or at least you will be as soon as you download the open source software called Audacity.  Most of you will be able to start using your home recording studio without spending a dime.  A few more of you may have to drop 4 or 5 bucks on the plastic PC mic.
With only the gear I just mentioned…a $4.00 mic plugged into the factory sound card of my computer, I recorded a song with guitars, lead vocal, and harmony vocals.  All of the audio recorded for this song never left Audacity.  This means that all of the editing and mixing was done with the tools already included in Audacity.
How did I do it?.  First, I recorded my acoustic guitar with the mic really close to the sound hole.  Then I sang along on a new track in Audacity while listening to the guitar.  Just “regular” sound cards these days are good enough to let you do this, though you’ll have to do a bit of editing to line everything up afterward.  Next, I recorded harmony vocals on some more tracks I added to the guitar and voice tracks.  After that, I adjusted some volumes, mixed them together (using only the tools in Audacity), and exported it as an mp3 file from Audacity.  Done.
This will give you an idea of what can be done at the “zero-to-five-dollar” budget level.  It isn’t the most spectacular audio ever.  But it isn’t half bad.  It’s certainly good enough for what a lot of folks need, audio-wise.
If you’re curious about how the song sounds, check out the video here:

Then when you’re ready to try this yourself, come see us at http://www.homebrewaudio.com