Most research in networked robots that use Web interfaces for robot control has been focused recently on the network part, since Ethernet involves poor (unpredictable) time performance. However, we believe that the problem to be addressed is more general and should not be restricted only to communication engineering: the interfaced system as a whole should adapt to get the most from the user, from the connection, and from the robot, even when no strict performance is possible. For that purpose, this paper introduces a new architecture for Web remote operation of robots that exhibits a high degree of flexibility in its adaptation to each particular user (through modular, configurable JAVA applets), to the system time-varying performance (through probability-guided, run-time adaptation of control loops), and to the robot software architecture (the standard CORBA is assumed as its middleware). Our approach constitutes an initial step for adapting comprehensively to all the mentioned issues, hence permitting to be employed in very different scenarios: realtime control, telecare, remote surveillance, etc.