You can find a list of free web hosting sites at http://www.free-webhosts.com you won’t need to register domain for almost all of them, I listed some that I think the best below.
If you don’t want ads in your website
http://www.phpnet.us/ and http://www.freewebtown.com are the best for you. http://www.phpnet.us/ gives you 300MB web space and 80GB bandwidth a month, no file size limit at all; while http://www.freewebtown.com is the only one that offers 2GB for free with no file size limit either, but the drawback is it only has 2GB bandwidth per month, the same as its space. if you want to get additional bandwidth you have to pay for it.
If you don’t care about the ads and you want a website with unlimited bandwidth and lots of space http://www.prophp.org is best for you, it gives you about 250MB space, no bandwidth limit and no file size limit either. The ad they put on your pages is only a banner on top.