The familiar code:
main
The essential difference between /* and / is that a servlet with mapping /* will be selected before any servlet with an extension mapping (like *.html), while a servlet with mapping / will be selected only after extension mappings are considered (and will be used for any request which doesn't match anything else---it is the "default servlet").
In particular, a /* mapping will always be selected before a / mapping. Having either prevents any requests from reaching the container's own default servlet.
Either will be selected only after servlet mappings which are exact matches (like /foo/bar) and those which are path mappings longer than /* (like /foo/*). Note that the empty string mapping is an exact match for the context root (http://host:port/context/).
See Chapter 12 of the Java Servlet Specification, available in version 3.1 at http://download.oracle.com/otndocs/jcp/servlet-3_1-fr-eval-spec/index.html.