ArcGIS Online(AGO) is a very nice tool for sharing, distributing, and building applications. One major thing it lacks is the ability to query, search, or find features within the web map. In my opinion this is essential to any application. Allowing an administrator to setup pre-defined searches for the end user. Additionally, I have seen some templates that have a query or search capability for features within the map but they require Feature Access/Feature Service. Currently this requires your data reside within an enterprise geodatabase. On the other hand Esri has been telling us that we would likely see better performance using a file gdb as a backend for our map services. I would think the same type of functionality like Query could be accomplished using a REST endpoint. Moreover, I think you should be able to publish a Feature Service using a file gdb as a backend and just disable the Create, Insert, and Update checkboxes if a file gdb is seen as a source during the publishing process. If AGO would just implement a search for map features I would dare say it is almost a complete package.
This idea has been merged with Ability to create queries in web maps.
I am a big proponent of AGO for its mobile editing capabilities, and I am looking forward to off line capabilities but until we get the ability to query, search, or find features within the map, I do not think AGO is as useful as it could be.