Delta, for one, makes a clear distinction between service animals and emotional support animals, and outlines documentation requirements for the latter.
Delta requires documentation (not more than one year old) on letterhead from a licensed mental health professional to be presented to an agent upon check in stating:
Title, address, and phone number of mental health professional.
The passenger has a mental health related disability recognized in the Diagnostic and Statistical Manual - 4th Edition.
That the passenger needs the emotional support or psychiatric service animal as an accommodation for air travel and/or for activity at the passenger's destination.
That the person listed in the letter is under the care of the assessing physician or mental health professional.
Lots of over-entitled people who may want to bring animals on-board free of charge will be stopped when they have to acknowledge having a mental health disability.