Well 304 is NOT_MODIFIED - "indicating a conditional GET operation found that the resource was available and not modified"
Now I am wondering if the GET is going all the way to Tomcat or if IIS is deciding that it doesn't need to.
You could change the Tomcat configuration to log ALL access - see the AccessLogValve inside the Host tag of service.xml file.
When I did that I was astonished at the number of web crawler accesses
Bill