As a hack, when I need an append-only datastore with no authentication or validation, I use Amazon S3. S3 is usually a read-only service from the unauthenticated web client's point of view, but if you enable access logging to a bucket you get full-query-parameter URLs recorded in a text file for GETs that can come from a form's action or via XHR.
There aren't a lot of internet-safe append-only datastores out there. All my favorite noSQL solutions divide permissions into read and/or write, where write includes delete. SQL databases let you grant an account insert without update or delete, but still none suggest letting them listen on a port that's open to the world.