If your SharePoint List or Library data connection returns an error in FormsViewer with the following text:

No adapter found for the name <Your Data Connection Name>

The most likely culprit is your form's compatibility! InfoPath changed the data structure for SharePoint List and Library data connections with the release of InfoPath 2010. Check your form's InfoPath version under Form Options > Compatibility. Set it to Web Browser Form (which is InfoPath 2013) and then walk through the data connection again to update the schema.