Use HTML5 to display PDF files if users don't have pdf plugin for their browsers.
Thanks to pdf.js project by Mozilla.
With this module you can use pdf.js to display PDF file all the time or only use pdf.js when visitors don't have pdf reader plugin.
About how to compile pdf.js on different platforms, please read this issue. For only using "PDF default" display, you don't need to compile pdf.js.
Because this module needs many front end works and I'm not good at HTML5, JS and CSS, if you want more advance features, please consider to be the co-maintainer.