We consider robust resource allocation of services in Clouds. More specifically, we consider the case of a large public or private Cloud platform such that a relatively small set of large and independent services accounts for most of the over-all CPU usage of the platform. We will show, using a recent trace from Google, that this assumption is very reasonable in practice. The objective is to provide an allocation of the services onto the machines of the platform, using replication in order to be resilient to machine failures. The services are characterized by their demand along several dimensions (CPU, memory,. . .) and by their quality of service require-ments, that have been defined through an SLA in the case of a public Cloud or fixed by the administrator in the case of a private Cloud. This quality of service defines the required robustness of the service, by setting an upper limit on the probability that the provider fails to allocate the required quantity of resources. This maximum probability of failure can be transparently turned into a set of (price, penalty) pairs. Our contribution is two-fold. First, we propose a formal model for this allocation problem, and we justify our as-sumptions based on an analysis of a publicly available clus-ter usage trace from Google. Second, we propose a resource allocation strategy whose complexity is low in the number of resources, what makes it well suited to large platforms. Finally, we provide an analysis of the proposed strategy through an extensive set of simulations, showing that it can be succesfully applied in the context of the Google trace.