This plugin lists similar to the current post based on the number of common categories.
This plugin adds a widget to WordPress that will list similar posts to the one being reviewed. The widget will only be rendered on a post single page, as otherwise it would not be relevant.
A shortcode is also available -- [magadanski-similar-posts]. There are several attributes available for the shortcode:
The similarity is considered based on the number of common categories for this posts and the rest of the posts in your blog.