Sometimes we want to see someone cool and edgy rather than conventional good guys.
“Antihero” usually refers to a character who does heroic things — but doesn’t fit the classic “good guy” definition.
Perhaps it's their motivation, lack of morals or outlook on life. Regardless of the reasons, we often find these characters interesting in their own way — let’s look at some of the examples.
Kiritsugu Emiya (Fate/Zero)
Kiritsugu is perhaps the textbook example of it. Jaded and disillusioned with the world and how much it is filled with death, he takes an utilitaristic approach to human life.
He is ruthless and unforgiving, but the anime does its best to show where he is actually wrong: the whole mindset makes no sense, and we should retain our humanity despite all odds.
Alucard (Hellsing)
Yes, “Alucard” is “Dracula” backwards. An ancient and incredibly overpowered vampire, he protects Britain — and the world — from supernatural threats. That does technically make him a good guy, but he certainly doesn’t act like one. To be fair, he has to deal with stuff like vampire Nazis.
Both the original series and the OVA, Hellsing: Ultimate are worth watching — though many fans prefer the latter, as it follows the manga more closely.
Lelouch (Code Geass: Lelouch of the Rebellion)
While Lelouch originally wants to just liberate his country, the scope of his plans increases many times. He already used many questionable methods in the beginning (his ability to control others doesn’t really have any applications that aren’t immoral), but the further he progresses, the thinner the line between an antihero and a villain protagonist becomes.
This is why we love Code Geass: Lelouch of the Rebellion (Code Geass: Hangyaku no Lelouch), though.
Accelerator (A Certain Scientific Accelerator)
Accelerator goes from being a crazy villain in one of the earlier arcs in A Certain Magical Index (Toaru Majutsu no Index) to becoming one of the most well-written characters in the entire franchise. Despite taking a more heroic stance, he isn’t actually any crazier and is often plagued by his past.
He focuses less on morals and order and goes out of his way to brutally deal with his enemies — according to Accelerator, he is a far better villain than any of them. He has his own spin-off in A Certain Scientific Accelerator (Toaru Kagaku no Accelerator), but he was a protagonist in some of the arcs in Index as well.
Dark Schneider (Bastard‼ Heavy Metal, Dark Fantasy)
Bastard‼ Heavy Metal, Dark Fantasy (Bastard!! Ankoku no Hakaishin) is an iconic — and somewhat infamous — manga that started back in the 80s. Following Dark Schneider, the evil wizard sealed in a teenage boy, it’s a story of epic and brutal action in a fantasy world.
Despite being supposedly evil, Dark Schneider is closer to an antihero — he often ends up protecting the innocent from threats that are even more evil. The manga is ridiculous (most of the names are references to actual metal bands), and the anime adaptation from a few years ago brought back attention to it.