I thought of Lima city, but they are a German hoster (website is in German, data centers are in Frankfort, Germany). I'm sure you will be able to find many others. Lima city is free (as in beer) and have unlimited storage[1], unlimited bandwidth, support PHP and MySQL, and allow you to add custom domains (you can buy them directly though them for very reasonable prices).

Although they are free, they have very little outages but they area limited to PHP (a big no-go for all my projects these days).

Disclaimer: I'm in no way affiliated with them except hosting my homepage there. I've used them for quite a few years now and they allowed me to show off my PHP projects to friends when I was 14 or so.

[1]: they have a fair use policy and downloads (everything except, html, PHP, css, js, and image files) are blocked and need to be hosted on their download server, which has a rate limit. They will also monitor your account for abuse (so if you consume a lot of bandwidth because you hid your download in the JPG file, they will ban you).