From the book "Release It!", the author describes an incident where an airline's entire check-in system went down for three hours, grounding its hundreds of planes and causing a pretty big backlog for hours more. The 'root cause' was code on the flight search server:

    lookupByCity(...) {
        ....
        try {
            conn = connectionPool.getConnection();
            stmt = conn.createStatement();
            ...
         } finally {
             if (stmt != null) {
                 stmt.close();
             }
             if (conn != null) {
                 conn.close();
             }
         }
    }

close() can throw, and in the circumstance of the outage it did for stmt, leading to the connection not getting closed and eventually the pool being exhausted with every thread blocked waiting for a connection. It's an interesting chain of failures, arguably the presence of such a chain is the real root cause, rather than the unhandled sql exception.