What is claimed is:1. A system, comprising:at least one processor; anda memory, storing program instructions that when executed by the at least one processor, cause the at least one processor to implement a stream management service, the stream management service configured to:retrieve, by a first stream processing worker of the stream management service, one or more data records from a partition of a data stream assigned by the stream management service to the stream processing worker, the one or more data records retrieved up to a buffer limit;update, by the first stream processing worker, checkpoint metadata for the partition of the data stream to indicate a pending checkpoint for the data records, the pending checkpoint indicating that the one or more data records are to be processed instead of skipped if a second stream processing worker is assigned to the partition of the data stream by the stream management service to replace the first stream processing worker; andafter sending the one or more data records processed by the first stream processing worker to a destination, update, by the first stream processing worker, the checkpoint metadata to advance the checkpoint as not pending, the not pending checkpoint indicating that the one or more data records are to be skipped if the second stream processing worker is assigned by the stream management service to the partition of the data stream to replace the first stream processing worker.2. The system of claim 1, wherein the update to the checkpoint metadata for the partition of the data stream to indicate the pending checkpoint for the data records includes, in the checkpoint metadata, a location to store the one or more data records in the destination.3. The system of claim 2, wherein the update to the checkpoint metadata to advance the checkpoint as not pending removes, from the checkpoint metadata, the location to store the one or more data records in the destination.4. The system of claim 1, wherein the update to the checkpoint metadata to advance the checkpoint as not pending is performed responsive to receiving an acknowledgement from the destination that the one or more data records are stored.5. The system of claim 1, wherein the buffer limit is specified via a request received via an interface for the stream management service.6. The system of claim 1, wherein the data stream is a managed data stream, wherein the partition is one of a number of partitions dynamically determined for the managed data stream in response to receiving a request to create the managed data stream.7. The system of claim 1, wherein the stream management service is further configured to access, by the first stream processing worker, the checkpoint metadata to identify the one or more data records to process and send to the specified destination.8. A method, comprising:retrieving, by a first stream processing worker of a stream management service, one or more data records from a partition of a data stream assigned by the stream management service to the stream processing worker, the one or more data records retrieved up to a buffer limit;updating, by the first stream processing worker, checkpoint metadata for the partition of the data stream to indicate a pending checkpoint for the data records, the pending checkpoint indicating that the one or more data records are to be processed instead of skipped if a second stream processing worker is assigned to the partition of the data stream by the stream management service to replace the first stream processing worker; andafter sending the one or more data records processed by the first stream processing worker to a destination, updating, by the first stream processing worker, the checkpoint metadata to advance the checkpoint as not pending, the not pending checkpoint indicating that the one or more data records are to be skipped if the second stream processing worker is assigned by the stream management service to the partition of the data stream to replace the first stream processing worker.9. The method of claim 8, wherein updating the checkpoint metadata for the partition of the data stream to indicate the pending checkpoint for the data records includes, in the checkpoint metadata, a location to store the one or more data records in the destination.10. The method of claim 9, wherein the update to the checkpoint metadata to advance the checkpoint as not pending removes, from the checkpoint metadata, the location to store the one or more data records in the destination.11. The method of claim 8, wherein the update to the checkpoint metadata to advance the checkpoint as not pending is performed responsive to receiving an acknowledgement from the destination that the one or more data records are stored.12. The method of claim 8, wherein the buffer limit is specified via a request received via an interface for the stream management service.13. The method of claim 8, wherein the data stream is a managed data stream, wherein the partition is one of a number of partitions dynamically determined for the managed data stream in response to receiving a request to create the managed data stream.14. The method of claim 8, further comprising accessing, by the first stream processing worker, the checkpoint metadata to identify the one or more data records to process and send to the specified destination.15. One or more non-transitory, computer-readable storage media, storing program instructions that when executed on or across one or more computing devices cause the one or more computing devices to implement:retrieving, by a first stream processing worker of a stream management service, one or more data records from a partition of a data stream assigned by the stream management service to the stream processing worker, the one or more data records retrieved up to a buffer limit;updating, by the first stream processing worker, checkpoint metadata for the partition of the data stream to indicate a pending checkpoint for the data records, the pending checkpoint indicating that the one or more data records are to be processed instead of skipped if a second stream processing worker is assigned by the stream management service to the partition of the data stream to replace the first stream processing worker; andafter sending the one or more data records processed by the first stream processing worker to a destination, updating, by the first stream processing worker, the checkpoint metadata to advance the checkpoint as not pending, the not pending checkpoint indicating that the one or more data records are to be skipped if the second stream processing worker is assigned by the stream management service to the partition of the data stream to replace the first stream processing worker.16. The one or more non-transitory, computer-readable storage media of claim 15, wherein updating the checkpoint metadata for the partition of the data stream to indicate the pending checkpoint for the data records includes, in the checkpoint metadata, a location to store the one or more data records in the destination.17. The one or more non-transitory, computer-readable storage media of claim 16, wherein the update to the checkpoint metadata to advance the checkpoint as not pending removes, from the checkpoint metadata, the location to store the one or more data records in the destination.18. The one or more non-transitory, computer-readable storage media of claim 15, wherein the update to the checkpoint metadata to advance the checkpoint as not pending is performed responsive to receiving an acknowledgement from the destination that the one or more data records are stored.19. The one or more non-transitory, computer-readable storage media of claim 15, wherein the data stream is a managed data stream, wherein the partition is one of a number of partitions dynamically determined for the managed data stream in response to receiving a request to create the managed data stream.20. The one or more non-transitory, computer-readable storage media of claim 15, storing further instructions that when executed on or across the one or more computing devices, cause the one or more computing devices to implement accessing, by the first stream processing worker, the checkpoint metadata to identify the one or more data records to process and send to the specified destination.