Get related node by taxonomy term?
I've used the 2.x version of Similar by Terms in the past, and it is very good, with nice views integration. A D7 version of the 2.x branch is in development at http://drupal.org/node/1270244.

The Apache Solr module can also supply a block of nodes that have similar taxonomy terms based on a Solr database: http://drupal.org/project/apachesolr. Very fast, but not trivial to set up. 

Finally, here's a comparison of similar/relevant content block modules: http://drupal.org/node/323329.