Bludit - Bludit is a web application to build your own website or blog in seconds, it's completely free and open source. Markdown support.
HTMLy - HTMLy is an open source databaseless blogging platform. A Flat-File Blog and Flat-File CMS written in PHP prioritizes simplicity and speed.
Grav - The modern open source flat-file CMS
BaferCMS - The fastest and the easiest way to edit content "in-place", while looking at the website.
BoidCMS - Flat file CMS for building simple websites and blogs.
Nibbleblog - Nibbleblog is a powerful engine for creating blogs, all you need is PHP to work.