This is a simple WordPress plugin which uses the awesome Colorbox jQuery plugin by Jack Moore.
It adds a link to the beginning of each of your posts when viewed on its individual post page. Clicking the link loads a totally clutter-free popup with just the post's content and some nice typography.
Click the "Reading Mode" link in the demo site here to see it in action.
To understand how it works, or to integrate it into your theme without a plugin, check out the tutorial.
Colorbox is licensed under the MIT license.
Everything else is under the GPLv2.