Yes its possible. I firstly advise get enough protection of your files you dont want accessed to the Web. You'd need a Firewall etc.
But yes its very possible
I found this thread on Tutorialforums. if you do a search for hosting on own computer you should find similar results
http://tutorialforums.com/showthread.php?s=&threadid=5014&highlight=hosting+from+own+computer
What it may not say is that you should Check with Your ISP if its ok.
If not you should get paid hosting.
Im not sure how true this is. But some hosts wont allow you to host a site on your own computer, and if done not only will they discontinue there service to you they may give you a fine. But i know the first bit is very true