Fair allocation has been studied intensively in both economics and computer science. This subject has aroused renewed interest with the advent of virtualization and cloud computing. Prior work has typically focused on mechanisms for fair sharing of a single resource. We consider a variant where each user is entitled to a certain fraction of the system's resources, and has a fixed usage profile describing how much he would want from each resource. We provide a new definition for the simultaneous fair allocation of multiple continuously-divisible resources that we call bottleneck-based fairness (BBF). Roughly speaking, an allocation of resources is considered fair if every user either gets all the resources he wishes for, or else gets at least his entitlement on some bottleneck resource, and therefore cannot complain about not receiving more. We show that BBF has several desirable properties such as providing an incentive for sharing, and also promotes high overall utilization of resources; we also compare BBF carefully to another notion of fairness proposed recently, dominant resource fairness.