1. A computer-implemented method comprising: configuring, by one or more computing systems of a service provider, a first private virtual computer network that is provided by the service provider and includes multiple computing nodes, the configuring including associating the multiple computing nodes with multiple network addresses from a plurality of network addresses specified for use with the first private virtual computer network, and further including assigning one of the plurality of network addresses separate from the multiple network addresses to represent, within the first private virtual computer network, a remote resource service external to the first private virtual computer network; restricting, by the one or more computing systems, communications sent by the multiple computing nodes to only destinations indicated by the plurality of network addresses; associating, by the one or more computing systems and with the assigned network address, an identifier that represents a location of the first private virtual computer network, wherein the identifier is an indicator supplied by the service provider for use by the remote resource service in validating that communications are sent from the location of the first private virtual computer network; modifying, by the one or more computing systems, a communication that is sent to the assigned network address by one of the multiple computing nodes to cause the modified communication to include the identifier; and forwarding, by the one or more computing systems, the modified communication to the remote resource service via one or more networks external to the first private virtual computer network.