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Free Hosts
All hosts below I have personally tried and used. They all support php, html and mysql.

000webhost Visit Website

000webhost.com ($0.00 webhost), is an industry leader in providing top class free web hosting services without advertising! There are no hidden costs, no adverts, and no restrictive terms. Lightning fast speeds, maximum reliability and fanatical user support are just a few of the features you'll receive with our service.
No Ads! (at all)
1500 MB of Disk Space
100 GB/month of Bandwidth
5 Add-on Domains
5 Sub-domains
5 E-mail Addresses
2 MySQL Databases
1 FTP Account (timeout of about 30 seconds)
Fast Speed

They remove websites for inactivity if your website does not get 10 visitors in 1 month. However they do send you a reminder to protect your website 2 weeks before removal. They also provide an option to "Resetup Your Account" (I do not know how long this stays up though).

Fii.me Visit Website

So, why FII? We have an all-inclusive prices and an unbeatable value Other web hosting companies promise cheap hosting, but then charge extra for setup fees, higher renewal or missing services, rates, or promotional services. With fii. It's all upfront!
No Ads! (at all)
10000 MB of Disk Space
100 GB/month of Bandwidth
? Add-on Domains
Limited Sub-domains
Unlimited E-mail Addresses
Unlimited MySQL Databases
Unlimited? FTP Account (seems to have no timeout)
Fast Speed

If your website has no visitors for 30 days then it will be deactivated.