I've come across a lot of users that have requested the ability to download ArcGIS Online Hosted Feature Services and ArcGIS Server Feature/Map Services. See that attached tool to do just this. The tool will also allow you to download attachments from ArcGIS Online Hosted Feature Services. Hope users find this helpful and useful.
Update 8/10/17: Tool will now download geodatabase coded value domains. Also, consolidatde the 2x and 3x version into one tool. The tool can be run from either ArcGIS Pro or ArcGIS Desktop.
Update 11/13/17: Tool now supports using a where clause to query the service.
Update 3/14/17: Updated to a single script for ArcMap/Pro using the requests module