Data stream ingestion and persistence techniques

A programmatic interface is implemented, enabling a client of a stream management service to select a data ingestion policy for a data stream. A client request selecting an at-least-once ingestion policy is received. In accordance with the at-least-once policy, a client may transmit an indication of a data record one or more times to the service until a positive acknowledgement is received. In response to receiving a plurality of transmissions indicating a particular data record, respective positive acknowledgements are sent to the client. Based on a persistence policy selected for the stream, copies of the data record are stored at one or more storage locations in response to one particular transmission of the plurality of transmissions.