Capabilities
The user can fully interpret and replicate the emotions, moods, and temperaments of others without reading apparent symptoms, allowing them to understand introverts or discover one emotion is actually hiding another. They can attack someone in a personal and emotional way since they know exactly what emotion is flowing through themselves and can use this knowledge to play against them. Some users may learn to read emotional imprints left into environment or objects.
Usually over time, an Empath's power grows to the point that they can manipulate emotions on others, and possibly use them to empower themselves. User may learn to extend their power over/on vast number of sentient beings or reach extreme distances, even other levels of existence but this may be possible only if the user has emotional link to those they search already in effect.
Variations
Empathy has many branches of power. Ranging from very weak to very advance. As the user becomes more advanced those branches may grow. Here are some levels that other empaths have displayed having/may gain:
Clairaudience - Some Empaths have displayed the ability to not only feel emotions, but also "hear" the heightened thoughts associated with that specific emotions. This is probably due to the fact that both cortices (emotional and mental) so closely relate to one another. An example would be if an empath senses two spouses aiming a lot of hatred towards one another. The empath might get the echo of thought along with that emotion (E.g. "I cant believe he's cheating on me after all these years"). However this is not to be confused with Telepathy. An Empath can only get visionary "echoes" related to certain emotions. They cannot read full memories.
Clairempathy - More advanced users of empathy have shown the ability to sense emotions over great distances such as cities, countries, continents, and other dimensions and planes (The Astral Plane AKA The Emotional Plane).
Clairvoyance - An Empath forges an emotional connection with another being. If that connection stays opens, the Empath is able to sense when that person is in danger and is also able to locate them by their "emotional scent". To give you an better understanding of this, one could consider this the empathic version of "Vampiric Siring" (see "True Blood", "Buffy", "Moonlight", and "The Vampire Dairies" for an understanding of supernatural "Siring"). See also Sensory Scrying
Empathic Illusion Casting - Empaths can create illusions based on certain emotions.
Empathic Healing - This is a level that is somewhat rare and not many can master. When an Empath "heals" wounds that are physical they don't heal the actual injury. The Empath simply takes the pain into themselves so the victim no longer feels that pain. However, Empaths can heal emotional wounds, but healing physical wounds is somewhat uncommon.
Empathic Mimicry - Higher level Empaths use this power to tap into others' abilities. This is done by the Empath channeling someone and finding the exact emotion that triggers their power. The Empath, so long as they remember that emotion, is able to use/copy that person's power, and maybe even turn powers against their users.
Empathic Power Absorption - Highly advanced Empaths can steal the powers of others for their own by using an associated emotion, leaving the victim powerless.
Empathic Power Randomization - Powerful Empaths can gain random powers based on their mood and emotions (gaining Regenerative Healing Factor or Invulnerability when scared, or Enhanced Strength when angry).
Empathic Projection - Some Empaths can develop the ability to project their own emotions onto others.
Intuitive Empathy - Unlike Empathic Mimicry where the user simply channels and copies others powers, Intuitive Empathy gives that user the knowledge to know how to use the ability intuitively.
Lie Detection - Empaths can sense when a person is lying to them, as lying can cause an irregularity in one's emotions. More skilled users and pick out what that lie is and find the truth.
Psychic Navigation - Empaths can sense a person by the emotional wavelength they give off or "empathic scent".
Psychometry - There are some places that have constant emotional residue (due to major events happening in that location war, death, historical moments, etc.). Some Empaths are able to tap into those emotional (lower level users that enter these places are overpowered involuntarily) imprints and re-experience those emotions as if they were happening in that moment. If skilled enough, some Empaths can also see the emotional echoes (images/residual ghosts) still there. This would be due to high levels of concentrated emotional energy.
Techno-Empathy - Empaths can sense the emotions of machines and other technology.
Telempathy - Empath can not only sense others emotions, but they can also send their own emotions to others. Users can communicate with one another emotionally and if skilled enough send "echoes" (ie: it means a quick glimpse of an image, e.g. sending the emotion of love to another user and the receiver seeing an image of their loved one like a mother, child, or spouse) of images back and forth.
Limitations
May only be able to receive emotions
Might get taken over and act on those emotions.
Inexperienced Empaths may find their powers completely useless in a fight.
May experience headaches.
May not be able handle large amounts of emotions at once.
Defenseless against beings that have no emotions, such as robots or users of Apathy.
May be easily possessed by Spirits and Ghosts, as they are beings bound with emotions.
This does not have to be an actual power, but can be a skill/ability that can be developed, though it rarely reaches the same level as the actual power.