Try including servlet-api.jar
as well.
java -cp bin\tomcat-juli.jar;lib\catalina.jar;lib\tomcat-util.jar;lib\servlet-api.jar org.apache.catalina.realm.RealmBase -a SHA passwd
EDIT
After trying to run this myself, there was yet another class missing. Instead of including every JAR in the classpath manually, I decided it would be easier to just include them all with lib\*
. Try this...it works for me!
java -cp bin\tomcat-juli.jar;lib\* org.apache.catalina.realm.RealmBase -a SHA passwd