This paper presents a resource management framework for providing predictable quality of service (QoS) in Web servers. The framework allows Web server and proxy operators to ensure a probabilistic minimal QoS level, expressed as an average request rate, for a certain class of requests (called a service), irrespective of the load imposed by other requests. A measurement-based admission control framework determines whether a service can be hosted on a given server or proxy, based on the measured statistics of the resource consumptions and the desired QoS levels of all the co-located services. In addition, we present a feedback-based resource scheduling framework that ensures that QoS levels are maintained among admitted, co-located services. Experimental results obtained with a prototype implementation of our framework on trace-based workloads show its effectiveness in providing desired QoS levels with high confidence, while achieving high average utilization of the hardware.