If you want to move a website from one web domain to another, you can use the Canonical tag in case you don't have access to the web server hosting that site to implement 301 redirects.
The Google Webmaster team has some useful advice for free hosting companies or websites that allow other users to create their own websites.
WordPress.com is a hosted service for blogs while TalkPress is a hosted service for online forums powered by bbPress, the free forums software from WordPress developers.
Dreamhost Apps offers free hosting for WordPress.org, MediaWiki, Drupal and other LAMP software. You can even use your free Dreamhost Apps account to use Google Apps for Web Domains.
Amazon S3 Tutorial: Learn how to hosting web images, css and other static files on to Amazon S3 Simple Storage Service.