1. A computer-implemented method for configuring intercommunications between computing systems, the method comprising: determining a virtual network to which an indicated program is to be associated, the indicated program to be executed on one of multiple virtual machines that are hosted by a first computing system associated with a program execution service, the first computing system being connected to a first of multiple physical networks of the program execution service that are configured to communicate via an interconnection network, the determined virtual network including computing systems on multiple of the physical networks of the program execution service; automatically enabling the one virtual machine of the first computing system to intercommunicate with other computing systems that are part of the determined virtual network, by: identifying a first networking identifier based on a first networking protocol that is associated with the determined virtual network and that is for use with the first physical network, and identifying a second networking identifier based on a second networking protocol that is associated with the determined virtual network and that is for use with the interconnection network; configuring a communication manager module for the first computing system to associate communications from the indicated program on the one virtual machine with the determined virtual network by using the first networking identifier with the communications; and configuring a networking device that connects the first physical network to the interconnection network to forward communications associated with the determined virtual network to the other physical networks that have computing systems that are part of the determined virtual network by using the second networking identifier with the forwarded communications; under control of the configured communication manager module, sending on the first physical network a communication from the indicated program on the one virtual machine, the sent communication on the first physical network being associated with the first networking identifier and being directed to a destination computing system that has a hosted virtual machine associated with the determined virtual network, the destination computing system being on a second of the multiple physical networks that is distinct from the first physical network; and under control of the configured networking device, forwarding the sent communication from the first physical network over the interconnection network toward the second physical network, the forwarded sent communication being associated with the second networking identifier.