Cluster systems are leading architectures for building popular Web sites that have to guarantee scalable services when the number of accesses grows exponentially. The most common Web cluster systems consist of replicated back-end and Web servers, and a Web switch that routes client requests among the nodes. In this paper, we propose a new scheduling policy, namely Multi-Class Round Robin (MC-RR), for Web switches operating at layer 7 of the OSI protocol stack. Its goal is to improve load sharing in recent Web clusters that provide multiple services such as static and dynamic information. We demonstrate through a wide set of simulation experiments that other dispatching policies aiming to improve locality in server caches give best results for traditional Web publishing sites providing static information and some simple database searches. On the other hand, when we consider more recent Web sites providing highly dynamic services, MC-RR is much more effective than state-of-the-art Web switch policies. The proposed algorithm has the additional benefit of guaranteeing stable results because its performance does not depend on several parameters that are very hard to tune in highly variable Web systems.