I flew on AA from jfk to lax, the woman next to me had a poodle wearing a sweater marked "service animal"--she claimed that she needed the dog for "emotional" support. My guess is that she had received some medical certification (from a Doctor(?)) affirming her and the dogs status.
My wife has a friend who brings her cockapoo along with an emotional support certification. The woman is actually crazy and on a cocktail of anti-depressants etc. Not all handicaps are visible. Emotions are a neurological state, and emotional disorders are a neurological condition.
That said, I am sure some people take advantage.