Sort nodes based on the amount of tags that match a specific node tags
Check out Similar by Terms module. This Drupal module attempts to provide context for content items by displaying a block with links to other similar content. Similarity is based on the taxonomy terms assigned to content. Blocks are available based on similarity within each of the defined vocabularies for a site as well as a block for similarity within all vocabularies. There are two methods of sorting. 1) Based on the most number of matching terms. 2) Based on lest used terms.

Or you could use the Relevant Content module. This module provides two ways of referencing relevant content. Both of these methods provide configuration to filter for specific content types and vocabularies, limit the maximum size of the result and provide some header text. The result on both cases are a list of nodes which the module considers most relevant based on the categorization of the current page. This is achieved by finding other nodes which are of one of the allowed types and have the most number of terms in common.