My mother swears that her 10 lb dog, Bunny, who is a Bichon-Poodle rescue, has a sixth sense for reading human emotions. Not only is she more attentive to both of my parents when they are feeling blue or under the weather, but she has a knack for sussing out people in need when they stop by for a visit. For example, even though Bunny is usually terrified of men (probably due to her pre-rescue past), when my parents' friend who had recently lost his wife to cancer came over for dinner, Bunny stood diligently by his side, occasionally licking his fingers as he sat and talked.
My cat, Rose (also a rescue), has a similar modus operandi. When I got my wisdom teeth out last year and suffered a subsequent infection, Rose planted herself by my face and gently licked the infected cheek for days until I recovered.
Temple Grandin, an adult with autism, wrote the book, Animals Make Us Human: Creating the Best Life for Animals, in which she discusses animals' emotional lives and their relationships with humans. Grandin asserts that animals' emotional lives are complex, diverse, and important.
I'm not exactly sure how much Bunny and Rose know or understand about peoples' emotions, but they have both proven time and again that they are aware of and interested in the emotional changes in the people they love. Not only are they aware, but they want to help. Sometimes it is hard to know what to say or how to act when someone we care about is struggling, so I suggest we learn a lesson from intuitive pets: just be there, stay calm, and offer the occasional lick (okay, maybe hug) as needed.