Since I’m using WordPress.com Stats, I would like to use the rankings generated by this service or plugin. Searching Google, I found some widget called "WordPress.com Stats: Top Posts Widget" which works out of the box (if like to use a widget). In my case I have a custom sidebar with different custom sections using custom code. The following example explains how-to use that code on your website.
WordPress, by default, doesn't track any statistic information about the posts on your site, so you'll need something like the WordPress Stats plugin to get that part working. Once that's there, you can use his code to pull out the posts from the last few days (configurable) and show the most popular of the list.