I have been looking for a reliable free web hosting provider for a long time, and after switching between multiple hosts, I have finally found a great site - www.x10hosting.com.
You get all the standard feature set, sometimes, more than what you get in paid hosting. The support forums are fantastic, the admin and mods are really helpful, and your queries are answered within the day. The speeds are also fantastic. What's more, if you haven't got large space and bandwidth requirements, you can even opt for an 'ad-free' package, and they don't modify any code in the web-pages you upload at all. You heard me right - no ads at all, not even the host's banners on the top or bottom of your page.
The main reason I switched from my last hosting provider to the above mentioned one was that the myphpadmin in the last one was abysmally, painfully slow. I haven't checked the new host's myphpadmin speeds yet, but, comparing the overall experience between my previous hosts and the current one, I can be reasonably sure that things will work out fine.
They seem every bit to be a professional hosting provider, and not some kid with a dsl connection, as I feel my previous hosts were.
You might want to check out its ratings and testimonials from other users here - *www.free-webhosts.com/reviews/X10Hosting.php
Edit -
Oh! And I forgot to mention they allow both sub-domains and TLDs.