How can I find files on Wikipedia (or the Wikimedia Commons) that are in two or more specific categories? For instance, if I was searching for files to put into the category "dogs and cats", I would want to find all of the files that were in both the category "dogs" and the category "cats." How can this be accomplished?
You can use CatScan to do that.
For example, to query files on Commons, you can start with http://toolserver.org/~magnus/catscan_rewrite.php?language=commons&project=wikimedia&ns=1 and enter the categories you want into the Categories box.