Get related node by taxonomy term? Let's say I have two content types: Page and News.   Both of them have a field called Tags which is taxonomy term.

Let's say I tag a page and a news item with the term 'celebration'.  When a user goes to the page on the front end website, the user should see related news items on the right side bar.  A news item is related to a page if they both have at least one tag in common.

I tried to set up a news item block, but i don't know how to tell it to show only news items that share at least 1 tag in common with the page.
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.