Free web hosting for academics

Both bitbucket and github allow you to publish a static website, which is handled under the same version control policies as everything else that you publish there.

You get no php/database support, but for academic web sites a static website generator such as Jekyll, which they both use, is more than enough.

Note added after reading @RebeccaJ.Stones comment to another answer: github is currently blocked in China, while bitbucket is not, so you may want to go for the latter, to make sure that everyone can access your website.

I recently created a website with Google Sites (https://sites.google.com/site/hadanylab/) and I think it was a good experience and a nice result. Easy to use, editing is the same as in Google Docs which is nice. Customization can be a pain, but that is expected. You can get around some of the difficulties using widgets, though.

I personally use altervista.org and I am satisfied with it. They give me 500MB space and 10Gb bandwidth for free, an address of the form yourname.altervista.org, run php 4 and 5 and a database service (with low performance in the free version), and allow a custom .htaccess. They offer paid upgrades and the option of putting banners for a revenue, but you can say no without any disadvantage.

They allow file upload only via (unencrypted) ftp, but you can automate that part easily.

It's not academics-specific, but as far as I can see neither is any other answer given up to now.