A system that implements a data storage service may store data for a database table in multiple replicated partitions on respective storage nodes. In response to a request to back up a table, the service may back up individual partitions of the table to a remote storage system independently and (in some cases) in parallel, and may update (or create) and store metadata about the table and its partitions on storage nodes of the data storage service and/or in the remote storage system. Backing up each partition may include exporting it from the database in which the table is stored, packaging and compressing the exported partition for upload, and uploading the exported, packaged, and compressed partition to the remote storage system. The remote storage system may be a key-value durable storage system in which each backed-up partition is accessible using its partition identifier as the key.