1. A computer-implemented method for executing programs for users in accordance with user-specified constraints, the method comprising: receiving a request from a user to execute one or more copies of a program specified by the user, the request including an indication of one or more execution constraints for use in selecting one or more host computing systems to execute the one or more specified program copies for the user, the one or more execution constraints being based on at least one of locations of the one or more computing systems and of capabilities of the one or more computing systems related to executing the one or more program copies; in response to the received request, automatically determining at least one candidate host computing system that is available to execute the one or more specified program copies for the user in accordance with the one or more execution constraints, the determined at least one candidate host computing systems being selected from multiple computing systems that are each configurable to execute any of a plurality of programs indicated by users of a program execution service, the automatic determining being performed by a configured computing device; automatically selecting the one or more host computing systems from the determined at least one candidate host computing systems to execute the one or more specified program copies for the user, such that each of the selected one or more host computing systems is to execute at least one of the one or more specified program copies, the automatic selecting being performed by the configured computing device; and automatically configuring each of the selected one or more host computing systems to execute the specified program, the automatic configuring being initiated by the configured computing device and including dynamically loading a copy of the specified program onto at least one of the selected one or more host computing systems, and initiating execution of the one or more specified program copies for the user on the selected configured one or more host computing systems.