For using This You Can Use Only Static Website Generator. Check Some Generators Here.
Github is my personal favorite. Github is used for code hosting but you can use it for hosting static website and static blog.
Simple Tutorial Blog is also host on github using octopress as a blogging software.
Bitbucket is used mainly for hosting a source code, but you can use it to host your static website.It’s like a GitHub so you can use either GitHub or bitbucket.
You Can Run Dynamic Website or Static Website Using Below Website’s.
Google App Engine is used for running your application in Google infrastructure.so you can set up a static website with it.Using This, You can also run a Dynamic website.Check here a tutorial by Mr.Amit Agarwal For Setup Own Web Proxy Using Google App Engine.
Heroku is a cloud application platform and support ruby, java, python etc.you can use it for host static or dynamic website. its work using a git system. It’s a very good platform and recommended by Facebook application.