A back story, when well done, can add depth to a character. If the author so wishes, a well written back story can even create sympathy for an antagonist by humanizing them. Warning: spoilers ahead.
By fleshing these characters out, the reader is forced to see them as more than antagonists, just like how in real life you’re more likely to sympathize with someone you know well than with a total stranger. You see the latter, despite all your best attempts, as less than a person, as more of an idea of a person. You still think of the people you know well as a collection of ideas, somewhat, but even then, because you know them well, you are able to see them as more than something to categorize (e.g. asshole clerk, anal retarded supervisor, maniacal driver who cut me off).
Even if a character is not made sympathetic, a back story can add to that character by emphasizing something important within the context of the story. The character of Voldemort in Harry Potter is revealed to be the result of a magical date rape drug. It is also implied that the lack of love that went into his creation, along with some bad genetics, gave rise to a child that never was capable of love, empathy, or trust. It works to further J.K. Rowling’s emphasis on the importance of those things, as the villain’s inability to experience them positions him in direct opposition to the values being espoused by the work.
All this is of course assuming that said back stories are written well.
A poorly written back story can detract from an antagonist, as it not only reflects poorly on the rest of the plot, but also makes the character less interesting.
This is especially true when giving back stories to antagonistic figures whose mystique lies in their enigmatic nature. Two particularly infamous cases are Hannibal Lecter and Darth Vader.
The former was fucking terrifying in Silence of the Lambs because he managed to get into peoples’ heads, and yet we barely knew anything about him. The following books and films ruined this by giving him a back story in an attempt to give him an excuse for why he is what he is. However, this was so poorly done that fans try to pretend they never happened.
In the case of Darth Vader, we actually had an idea of Anakin Skywalker’s downfall, but simply having a general idea and watching Darth Vader redeem himself at the end was enough. The prequels tried to show his tragic downfall, but the clumsy execution only made me wish I’d never seen them (although I do like Revenge of the Sith, for all its flaws).
Other villains who benefit from a lack of back story include Anton Chigurh and Heath Ledger’s Joker, as the lack of detail given to their histories makes them appear less as people and more as malevolent entities who may be better described as terrifying forces of nature.
In such cases, less really is more.
Freudian excuses can sometimes be one of the laziest ways an author can characterize a villain. Oftentimes, a single childhood trauma is supposed to be enough to justify why a character grew up to be a mass murderer.
Alan Moore, genius that he is, mocked the idea in his seminal Batman story The Killing Joke as well as within this rather sarcastic passage:
“I was just standing there, looking at my stamp album and the priceless collection that it had taken me years to build, when all of a sudden I realized that since I had foolishly pasted all of them directly into the album using an industrial-strength adhesive, they were completely worthless. I understood then that the universe was just a cruel joke upon mankind, and that life was pointless. I became completely cynical about human existence and saw the essential stupidity of all effort and human striving. At this point I decided to join the police force.”
The point is that a character should not be defined by a single issue, but should instead be a rich tapestry consisting of how innate characteristics interacted with their environment. A back story that relies on a single trauma to justify a character becoming evil is often a waste of ink and time.
The case of Johan Liebert from Monster is a spectacular subversion. While the series does explore what goes into the creation of a “monster”, as well as the true face of human nature, in the end it is clear that while Johan went through some serious trauma, other factors suggest that perhaps there was already something rotten within him from the beginning.
The point I’m making is this: back stories can add depth to a character when done right. However, they are not always necessary when attempting to craft a great antagonist. A back story is in the end a trope, and as a certain website puts it: tropes are tools. Tools that can be used wisely or poorly whether in their usage or absence.