Google's dictionary defines empathy simply as "the ability to understand and share the feelings of another", but in reality, empathy is much more complex than that. It's essential for healthy human relationships and communication. Empathy is not unique to humans, as other primates have been found capable of empathy, expressed in the form of consoling other members of their species  — and I'm sure anyone who lives with cats or dogs is as sure as I am that they feel it too. Empathy is, however, essential to the human experience.
Hyper Empathy: Is There Such A Thing As Too Much Empathy?
Empathy is a good thing, right? For a much-understudied subgroup of people, however, emotional empathy is so deep and overwhelming that they go far beyond understanding what another person is feeling, this empathy affecting their own feelings, and their empathy leading them to reach out and help their fellow humans. Rather, they "soak up" the feelings of others — often even relative or complete strangers and fictional characters — to the point they may actually physically share someone else's pain.
It's hardly a surprise that some people have come to refer to this phenomenon as hyper empathy syndrome. Research reveals that this excessive empathy is sometimes the result of conditions like Borderline Personality Disorder , Sensory Processing Sensitivity , and Autism Spectrum Disorder .
In case that last one surprises you, research has found that while autistic people may take longer to accurately read someone else's emotions (known as cognitive empathy), they have absolutely no problems "feeling with" a person once they understand their emotional state (known as affective empathy) . Adults with Asperger's and too much empathy are, in particular, not very hard to come by.
Then there was the case of a woman who suddenly developed seemingly super-human empathy after brain surgery for epilepsy. Part of her amygdala, the feeling and decision-making center of the brain, was removed, and this sent her empathy into overdrive — even being overwhelmed by the emotions of fictional characters. 
Still, many folks who don't have other diagnosable mental or physical disorders can also be hyper empathic. Since hyper empathy disorder isn't currently part of any diagnostic manual, and treatment hasn't been explored, the best these people can do is learn how to control negative and positive emotions with hyper empathy disorder.
Empathy Deficit Disorder: That's Just Psychopaths, Right?
Think of people who don't experience empathy, and the term "psychopath" is bound to enter your mind in a matter of seconds. People with Antisocial Personality Disorder, the official term for what's known as psychopaths in popular vocabulary, are ego-centric; their sense of self derived from power and personal pleasure. One of the diagnostic criteria for Antisocial Personality Disorder is indeed a "lack of concern for feelings, needs, or suffering of others; lack of remorse after hurting or mistreating another". 
This doesn't mean that people with this diagnosis don't understand the feelings of others, by the way — they don't lack cognitive empathy, and are skilled at using it to their own advantage. It's affective, or emotional, empathy that people with Antisocial Personality Disorder lack. They know what you're feeling, but if it doesn't suit their agenda, they simply don't care. 
Psychopaths aren't the only people who can suffer from an empathy deficit, however.
- People with Post-Traumatic Stress Disorder may have become so desensitized to the suffering of others, and their trauma may have interfered with their capability to feel the full spectrum of emotions themselves, so much that they lack affective empathy. 
- Those with Narcissistic Personality Disorder have deficits in affective empathy while being fully capable of cognitive empathy. 
- Children and adolescents with Conduct Disorder, a serious disorder that leads to aggressive and other socially unacceptable behavior, have been found to have empathy deficits as well. 
- The emotional empathy of alcoholics was revealed to be impaired, while cognitive empathy remains intact. 
Before you, as a person of normal or hyper empathy, start thinking of these people as cold-hearted, wait a second — I bet you've experienced a lack of empathy (or selective empathy, if you like) in certain contexts yourself. Research indicates, for instance, that white people are more likely to become distressed at at the pain of another white person than the pain of a black person . We're not talking about overt and conscious feelings of racism here, but about implicit bias. In the same way, I daresay that most people "feel the feels" much more when a natural disaster hits a place they somehow identify with than when disaster strikes a location they wouldn't even be able to find on the map. We're more empathic, generally, if we can personally relate to the people who are the targets of our empathy.
I Think I Need Help!
Do you think you're excessively empathic and you'd jump at the chance to receive testing for hyper empathy syndrome if such a diagnosis existed? Can you recognize other people's emotions analytically, but have you lost the ability to really feel with them? Or do you sometimes have trouble adequately judging another person's mental state, but deeply care about people nonetheless?
Maybe you qualify for a related diagnosis — such as PTSD, Autism Spectrum Disorder, or Sensory Processing Sensitivity. Maybe you don't, but you don't need an official diagnosis to be able to see a therapist. If you've recognized that there's "something wrong with you", talk therapy can help you regardless.