Getting "Oracle ORA-00018: maximum number of sessions exceeded"

Problem

Using an Oracle database you see database exceptions in SystemOut.log, which look similar to: [12/20/05 15:40:12:708 EST] 33404031 FreePool E J2CA0046E: Method createManagedConnctionWithMCWrapper caught an exception during creation of the ManagedConnection for resource jdbc/DMDDS, throwing ResourceAllocationException. Original exception: com.ibm.ws.exception.WsException: DSRA8100E: Unable to get a PooledConnection from the DataSource. with SQL State : 60000 SQL Code : 604 at oracle.jdbc.dbaccess.DBError.throwSqlException(DBError.java(Compiled Code)) at oracle.jdbc.ttc7.TTIoer.processError(TTIoer.java:289) ... Caused by: java.sql.SQLException: ORA-00604: error occurred at recursive SQL level 1 ORA-00018: maximum number of sessions exceeded DSRA0010E: SQL State = 60000, Error Code = 604DSRA0010E: SQL State = 60000, Error Code = 604 ... 55 more ---- Begin backtrace for nested exception java.sql.SQLException: ORA-00604: error occurred at recursive SQL level 1 ORA-00018: maximum number of sessions exceeded DSRA0010E: SQL State = 60000, Error Code = 604DSRA0010E: SQL State = 60000, Error Code = 604 at oracle.jdbc.dbaccess.DBError.throwSqlException(DBError.java(Compiled Code)) at oracle.jdbc.ttc7.TTIoer.processError(TTIoer.java:289) at oracle.jdbc.ttc7.O3log.receive2nd(O3log.java:496) at oracle.jdbc.ttc7.TTC7Protocol.logon(TTC7Protocol.java:278) at oracle.jdbc.driver.OracleConnection.(OracleConnection.java:346)