In The Vampire Diaries, the antiheroes have a very important role in the storyline, as their actions and stories have a great impact on the protagonists and antagonists.
An antihero (sometimes antiheroine as the feminine) is generally considered to be a protagonist whose personality can be perceived as being villainous and heroic at the same time, in contrast to the more perpetually noble characteristics of an archetypal hero or the perpetually immoral characteristics of an archetypal villain.
They are generally expected to be more physically attractive, stronger, braver, cleverer or more charismatic. Unlikely heroes are simply characters who may not be conspicuously flawed, but simply ordinary people thrust into extraordinary circumstances.
They may be corrupt, oppressive, etc., or may merely have no unusual qualities whatsoever (the common definition). They are not villains but not necessarily heroes. They may do bad things but are not evil. They may fight villains, but not for the reason of justice, or if it is for the cause of justice will take an "ends justify the means" stance. Their actions are motivated by their own personal desires, such as revenge.
Damon Salvatore - is the older brother of Stefan Salvatore, and friend of Elena Gilbert, as well as Bonnie McCullough, Meredith Sulez, Matt Honeycutt, and Sage. In the first book, The Awakening, Damon remains in the shadows watching Stefan and Elena. During the invocation/session by Bonnie, to know who is going to marry Elena, Damon enters the McCullough house, Damon proves to be friendly and affectionate with Elena, but the meeting ends, Damon disappears and the Bonnie's dog is found dead (Elena thinks it was Damon). During the celebration of Halloween, Damon appears again, but on this occasion Damon kills Mr. Tanner. In the second book, The Struggle, Damon tries to convince the Gilbert family that he is the best option for Elena. Elena asks Damon to help her stopping Tyler and Caroline from revealing her secrets to the whole school. In the third book, The Fury, Damon put aside the rivalry to his brother to protect and care Elena. For a time, Damon shows Elena, that he is not bad, but he do not want to show his noble side. During the final battle, Damon does his best to protect Elena, and his brother, but in the end Katherine and Elena die. In the last book of the original series, Dark Reunion, Stefan is invoked by Bonnie, and Damon accompanies his brother, with the excuse that he was also invoked (In the end of book, Matt reveals that Damon was never invoked). During our guard to protect Vickie, Damon did his best to stop Klaus, but the problem is that he was never invited to the Bennett house and felt guilty. Damon disappears after the tragedy, but returns to help his brother and friends against Klaus.
TV Series Characters
Damon Salvatore - is the older brother of Stefan Salvatore, boyfriend of Elena Gilbert, former friend of Alaric Saltzman, and an ally of Caroline Forbes, Bonnie Bennett, Jeremy Gilbert, Matt Donovan, and Tyler Lockwood. In Season One, Damon was a main antagonist, but eventually becomes a protagonist, and finally an antihero (Season Two) and later a tritagonist. Damon's actions were those of a murderer, and was intended only to hurt his brother, in revenge for forcing him to be a vampire. Eventually, he was falling in love with Elena Gilbert, a young woman as the same physical appearance of Katherne Pierce, but with benevolent personality. Damon always proved to be hard, cold, calculating, without positive feelings, even Elena mentions that for him, the love relationships always end badly. For a time, Damon tried to be good, helping others, protecting them from other vampires, and werewolves, but his actions did not have the desired results, so decides remain neutral, helping his brother and friends against supernatural threats, but in order to protect Elena.
Elijah Mikaelson - is one the first vampires of the New World. He is son of Mikael and Esther, as well as older brother of Niklaus, Kol, Rebekah, Henrik, and little brother of Freya, Finn. In the Season Two, Elijah is cold, calculating, evil, vindictive, but remains noble, and prudent in dealing with respect to his enemies. Over time, Elijah feelings for Elena, as well as respect for Stefan, Alaric, and Bonnie. During the confrontation against Niklaus, Elijah betrays his word to destroy his half brother in order to find his family. Months later, Elijah returns and helps the protagonists to face Niklaus, Elijah helps Damon to wake his siblings, to confront the original hybrid, but the arrival of Esther cause Elijah remains neutral. Elijah discovers plans of the original witch, and Elena, causing the back becomes evil, but eventually reconsiders and understands what Elena, and Esther trying to do. At the end of Season Three, Elijah returns to help his family, but also protect Elena from his siblings. Unfortunately, Elijah lost his half-brother, and his sister in revenge kills Elena.
Niklaus Mikaelson - is one of the originals and is an original vampire werewolf hybrid. At first, his main goal in mystic falls is to break the curse put on him and sacrifice elena to do so. He later helps Stefan heal Damon only to use Stefan to his own gain. Later on, he heals Caroline from a werewolf bite but again could be seen as for personal gain. After Esther is freed and the realization of the bloodline is noticed, Klaus teams with the mystic falls kids to stop Esther and Alaric. He then teams with Stefan, Damon, Bonnie and Jeremy to stop Alaric and in a rare moment, saves Caroline instead of taking advantage of her. Later on, he provides hybrid bodyguards for Tyler, helps Damon to stop Connor and heals Elena. Many other traits of him are seen as anti heroic, as the case in many situations where he could have killed his enemies but let them live. He seems to also grow softer and more human around Caroline but can switch back to evil in a heartbeat.
Both in the novels and the TV series Damon is an antihero.
All the characters that are considered antiheroes are at least part vampire.
The Mikaelson family (especially Klaus) were often considered to be the main antagonists of the Vampire Diaries series. However, in the second half of season 4, Kol is killed and the three remaining siblings eventually leave Mystic Falls to settle back in New Orleans and ultimately end up becoming the main protagonists of their own series, The Originals.
Niklaus Mikaelson and Damon Salvatore were both main antagonists who ultimately became main protagonists.
Generally, anti heroes are hard to identify, because their motives, actions, and purposes. Damon, and Katherine were antagonists in the early parts of Season One and Two respectively, after the second part of the seasons, they committed acts that seemed bad, but ultimately were justified, by saving the lives of their loved ones, or to defeat the enemies. Elijah is a bit different compared to Katherine and Damon. In the second part of Season Two, Elijah acts cruel, cold and calculating, even, it may think that he has no feelings for other beings, but after Elena withdrew the dagger and spent almost a whole day with him, he sees the love and loyalty to her family, friends, and boyfriend, causing Elijah decided to join the protagonists to destroy Niklaus. Some time later, Elijah returns, and again is an ally, but betrays the protagonists to save his family, but reconsiders and decides to help save the lives of his family and of Elena (End of the Season Three).