1. A method for a computing system to provide logical networking functionality for computer networks, the method comprising: receiving, by one or more configured computing systems of a configurable network service, configuration information that specifies a quantity of multiple computing nodes arranged via a specified network topology for a first virtual computer network, the network topology including multiple sub-networks that each include a distinct subset of the multiple computing nodes and are each associated with one of multiple specified physical router devices; implementing the first virtual computer network in accordance with the received configuration information by overlaying the first virtual computer network on a distinct physical substrate network that interconnects the multiple computing nodes; receiving, by the one or more configured computing systems, one or more requests from a respective one of the multiple computing nodes for information from the specified physical router device associated with a respective one of the multiple sub-networks that includes the respective one computing node; responding, by the one or more configured computing systems, to each of at least one of the received requests by emulating functionality of the specified physical router device in generating response information for the respective one computing node without using any physical router devices to represent the specified physical router device; and forwarding, by the one or more configured computing systems, a communication from a sending computing node of a first of the multiple sub-networks to a destination computing node of a distinct second of the multiple sub-networks by emulating further functionality of the specified physical router device for modifying the communication as part of the forwarding.