Free hosting just may not be what you need. But it has come a long way and somewhere it does exist, possibly providing a need or niche for testing web apps under a different server configurations, or just testing out a simple website idea.

Here's a short list of links I put together that provide PHP/MySQL hosting and information.

If you want to keep it simple:
Leads for free php hosting -

http://Zymic.com
http://000WebHost.com
http://110MBHosting.com
http://freedrupal5hosting.com/
http://lazbit.com/
http://www.mysitepages.com/
http://www.hostbot.com/
http://www.oxyhost.com/
http://www.0php.com/free_PHP_hosting.php
http://www.hostadfree.org/
http://www.mister.net/
http://www.agilityhoster.com/
http://www.free-webhosts.com/webhosting-01.php
http://www.byethost.com/free-hosting
http://www.free-site-host.com/

The motherload of all free host info,
Been around for a long time:

http://www.freewebspace.net
(good resource to get user ratings)

Rated and Reviewed given you got the time to put yourself to sleep.
http://www.freewebspace.net/free/Free-webhosting

If you are serious about wonky public server testing //
Here's the Next Level: If you really kinda wanna get nitty-gritty and downright free in the serious free php hosting world, then POST a request of what ya wanna do in here (esp. if you have specific requirements / you'll get responses! :)
Ask for your specs and you shall recieve an answer -
http://www.freewebspace.net/forums/forumdisplay.php?s=13f28e7303edc4e848...
If you really want something or are looking for something specific search through the forum or post a spec requirement in the forum link above. There are some serious geekmos in there.

A few slightly alternative approaches:
https://www.nearlyfreespeech.net/services/hosting.php
https://www.nearlyfreespeech.net/estimate
http://freedns.afraid.org/

http://www.freewindowshosting.org/

and quick list of
?free domains:

http://www.co.cc
http://www.freedomain.co.nr/
http://www.joynic.com/

// Point to note, like many things, that unfortunately, I cannot vouch for any of these hosting companies, or entities, and I am in no way affiliated with them. Just sayin.  // So use at your own risk //