This week's book giveaway is in the OCPJP forum. We're giving away four copies of OCA/OCP Java SE 7 Programmer I & II Study Guide and have Kathy Sierra & Bert Bates on-line! See this thread for details.
You can use static variables -- as long as their read-only (final). The reason for not being allowed to use read-write static variables is that the EJB container would have hard time synchronizing the static variable across the cluster.