Xtreemhost offers FREE webhosting plans that are completely ad-free and support PHP and mySQL databases. There are a few limitations however they are pretty generous. For example there is a 4mb file size limit, 5.5gb of web space and 200gb of bandwidth per month. View the plans here for the complete run down.
I haven’t signed up to test it out yet but I did look through the sign up process and it requires that you register a ‘.co.cc’ domain name (which is also free).
I see no reason why you couldn’t point an existing domain that you already own to your free hosting account if you don’t want to use a ‘co.cc’ domain and I plan to test this theory out soon on a small website I am planning to do for my Mum!
Xtreem hosting also offers a premium plan through their partner; FatCow, the premium plan goes for a tiny $44 per year and includes unlimited web space and bandwidth and no file size restrictions. It also claims to be powered by 100% wind energy which is good, I suppose?