1. A method for a computing system of a resource access manager service to manage access to computing-related resources based on multiple access policies specified by multiple distinct parties, the method comprising: receiving information about multiple resource provider services that each provide computing-related resources of one or more types for use by remote software applications over one or more networks; for each of multiple software applications, receiving configuration information indicating one or more of the multiple resource provider services that the software application is configured to use, such that executing copies of the software application use computing-related resources provided by the indicated resource provider services on behalf of users of the executing software application copies, the received configuration information specifying a baseline access policy by the software application for each of the indicated resource provider services such that each baseline access policy for a software application and an indicated resource provider service includes one or more constraints to control later access to the computing-related resources provided by that indicated resource provider service that are used by the executing copies of the software application; and storing the specified baseline access policy for later use; for each of multiple users, receiving subscription information from the user for subscribing to use an executing copy of an indicated software application, the received subscription information specifying an access policy by the user for the indicated software application that includes one or more constraints to control later access to computing-related resources used by an executing copy of the indicated software application on behalf of the user; receiving an access request that is from an executing copy of one of the multiple software applications to obtain access on behalf of one of the multiple users to an indicated computing-related resource from one of the multiple resource provider services, such that the one resource provider service is indicated in the received configuration information for the one software application and the one software application is indicated by the one user in the received subscription information from the one user; automatically determining whether to authorize the access request by, obtaining the stored baseline access policy specified by the one software application for the one resource provider service, and obtaining the access policy specified by the one user for the one software application, the obtained baseline access policy and the obtained access policy specified by the one user being unrelated to each other and being specified in a manner independently of each other; and determining whether the access request satisfies the included constraints of each of the obtained access policy specified by the one user and the obtained baseline access policy specified by the one software application; and if it is determined that the access request is authorized, automatically providing the access to the indicated computing-related resource on behalf of the one user to the executing copy of the one software application.