1. A method, comprising: providing, by a block storage service, block-level storage to a plurality of distinct computing instances for a plurality of distinct users; providing, by the block storage service, a backup copy function for creating backup copies of data stored in said block-level storage by said plurality of distinct computing instances for said plurality of distinct users, and storing the backup copies in different destination locations specified by respective ones of said plurality of distinct users; receiving, by the block storage service, input from a particular one of said plurality of distinct users specifying a particular destination for storing a backup copy of at least a portion of data stored in the block-level storage for said particular one of said plurality of distinct users; creating the backup copy of the at least a portion of data stored in the block-level storage for said particular one of said plurality of distinct users and storing to the particular destination the backup copy of the at least a portion of data stored in the block-level storage for said particular one of said plurality of distinct users; receiving, by the block storage service, input from another one of said plurality of distinct users specifying a different destination for storing a backup copy of at least a portion of data stored in the block-level storage for said another one of said plurality of distinct users; creating the backup copy of the at least a portion of data stored in the block-level storage for said another one of said plurality of distinct users and storing to the different destination the backup copy of the at least a portion of data stored in the block-level storage for said another one of said plurality of distinct users; and wherein the particular destination and the different destination are for different storage systems remote from one another.