I accidentally came across a plugin that was perfect for a project that I was going to be working on. I liked it so much that I decided to try it out on this site.
The plugin is called Related Posts Thumbnails. It uses the featured image and will relate posts based on categories, tags, both or randomly. Typically, a plugin will related based on categories or by tags so it was great to find one that provided the option to use one or the other. Personally, I prefer to use categories because I currently have too many tags and I get better matching results when I use categories.