Solomon Kane is the poster child for this trope, spending almost every story tramping around Darkest Africa all alone except for the Witch Doctor N'Longa, who he sees very infrequently, and various other characters whose main function, generally speaking, is to die violently.
Roland Deschain, the protagonist of Stephen King's magnum opus The Dark Tower, suffers from this trope: he has been alone for so long in his quest to reach the titular Dark Tower that it is his only reason for living. In the first book he goes so far as to let a twelve-year-old boy he rescued and bonded with to fall to his death, just to because his nemesis said it was the only way he'd ever allow himself to be caught, and said nemesis seemed to know about the Dark Tower. Roland's character softens into something a great deal more sympathetic after he forms a traveling party that helps him in his quest — which includes what amounts to a resurrected version of that kid, who'd have to be insane to follow Roland again under any other circumstances.
Susannah is clearly thinking of this trope when she thinks about how "the desert made him strange."
A key plot point throughout the series is that Lord Voldemort's lack of understanding of and inability to love another person or thing is one of his greatest weaknesses (he's actually a full-blown sociopath), whereas Harry's ability to love is his greatest strength. That said, Harry is a bit of a loner, of the more harmless variety. In fact, he is often mistaken for a freak, particularly in books 2 and 5, and his relatives think he's one too. This is due to his lonely childhood and his losses driving him to do everything himself so he doesn't risk others getting involved and losing them. Voldemort was also said to be quite popular when he was younger, and his followers, the Death Eaters, include many people he knew from school, although he tended to dominate his underlings and by the time he comes back its clear that most only hang around him out of sheer terror.
The young Severus Snape is also depicted as a loner due to his appearance and attitude as well as his aptitude for dark magic. Despite having Harry's mom, Lily as a friend and in fact him loving her, his choices drive her away and he ends up alone. He along with Harry and Voldemort are considered to be J. K. Rowling's three "abandoned boys."
Myrtle Warren became a "freaky little" nerd when she was teased by a girl named Olive Hornby, a school bully. Before she died, she cried in the bathroom.
In the last book, Dumbledore is revealed to be a true loner himself. While adored by the entire wizarding populace, Albus never seemed particularly close to anyone- the most fondness we see him express over the series is for his old flame Grindelwald and for Harry. Part of this is explained because his genius made him feel isolated, but by the last book, it becomes very clear he didn't trust anyone with all of his secrets, preferring to kill Voldemort with a Gambit Roulette. While Dumbledore is adored by all, most of the time, his intense quirkiness can lead to him being seen as a freak, as throughout The Deathly Hallows, Harry grows increasingly disillusioned as it sinks in how little Albus trusted him. However, this is ultimately a Downplayed Trope with him and we see Harry reconcile with Dumbledore when we see Dumbledore reflect on how this attribute caused him grief. Rowling says on Pottermore that Albus Dumbledore and Professor McGonagall were quite close, bonding over similarities in their childhoods. Albus and Aberforth Dumbledore were also reported to be relatively close before Grindelwald came and the Dumbledore boys lost their sister.
Luna Lovegood lampshades it when she says she has no friends because everyone thinks she's weird. But in the Deathly Hallows we see that she has gained five friends; Harry, Hermione, Ron, Neville and Ginny.
Ender's Gamedoubly subverts this. Everyone intentionally isolates Ender to make him a more efficient commander. Which also makes him an asocial freak that he never really gets over. But useful!
Ender's Shadow goes back on this a bit, playing up the fact that Ender relied on his army while Bean was the real antisocial genius. Or, to be more accurate, Ender could project all the leadership qualities and bind their loyalty to him but was completely alone himself, except for Bean, who had no idea how to really connect to other people. This is something of a plot point and stated outright: Ender takes down his bogeyman by himself whereas Bean has learned how to form a team that may or may not actually like him, but accept him.
The subsequent Shadow books do this even more clearly. Who's the villain? Achilles, who seems to be able to make everyone, except some of the battleschoolers, love him. He feels no attachment to them and is noted by Bean near the end as being empty and unable to understand true bonds. Who're the heroes? Bean, Mr. Antisocial himself, although it is revealed that his detachment from humanity is more about him caring too much than too little. And Peter Wiggin, the terror of his brother's life and the ultimate "I can do it myself" loner. Until he realizes just how good his parents are to talk to and after he marries Petra.
Harry Dresden of The Dresden Files is a loner of the harmless variety. He has a small circle of friends, but he's more or less antisocial, only being immediately nice to pretty girls (not because he's a pervert, he's just the chivalrous type). People treat him as a freak, but not because he's a loner. It's because he publicly advertises his being a wizard and people think he's nuts. This is only really an issue in the first four books. During and following Summer Knight, Harry finally accumulates enough True Companions that he can no longer really be considered a loner.
Subverted in The Andromeda Strain. The Odd-Man Hypothesis states that unmarried males should be given command during times of crises, as their lack of attachment allows them to make the most unbiased decisions.
Played frustratingly straight in the Kitty Norville series. Werewolves do not do well without a pack, and the further from civilization and multiple friendships, the worse the resulting monster becomes.
Played with in any Ayn Rand novel. Typically, villains or idiots believe this trope to be true, and most of the heroes are loners. The loners themselves consider the trope false, although they tend to get along with each other. Ultimately, Rand tends to invert this trope, although some of her heroes (Francisco d'Anconia in Atlas Shrugged and Austen Heller in The Fountainhead for example) are pretty sociable.
Speak: This is the reason Melinda is spurned by her classmates at school, other than the police-calling incident.
Everworld: Senna Wales. The first book, Search for Senna notes that she "was not the most popular girl at school." She doesn't allow anyone to know anything about her personality or motives at first, not even her boyfriend, David Levin. Later in the book it becomes apparent that she is an antisocial, scheming witch who is running her own plans. And that's the first thing we learn about her.
It was said later that he came under bad influences at this stage. But the secret of the history of Edward d'Eath was that he came under no outside influences at all, unless you count all those dead kings. He just came under the influence of himself. That's where people get it wrong. Individuals aren't naturally paid-up members of the human race, except biologically. They need to be bounced around by the Brownian motion of society, which is a mechanism by which human beings constantly remind one another that they are ... well ... human beings. He was also spiraling inwards, as tends to happen in cases like this.
Played with in A Hat Full of Sky. Witches tend to dislike other witches nosing in on their business, and it's repeatedly made clear that witches are not necessarily people people ("among the people, but not of the people"), but it's still important for them to visit each other occasionally to make sure they haven't gone bonkers. Their internal society is often compared to cats; more a set of individuals that tolerate each others company than an actual group.
Ossie Brunt in Jingo, who is basically the Disc's Lee Harvey Oswald:
It was not that Ossie was insane in any way. Friends would have called him a quiet sort who kept to himself, but they didn't because he didn't have any friends. There was a group of men who went to practice at the archery butts on Tuesday nights, and he sometimes went to a pub with them afterwards and sat and listened to them talk, and he saved up once and bought a round of drinks, although they probably wouldn't remember or maybe they'd say "Oh ... yeah ... Ossie." People said that. People tended to put him out of their minds, in the same way that you didn't pay much attention to empty space.
Sherlock Holmes arguably embodies the loner trope, with the exception of Dr. John Watson. That said, he and Watson were introduced by a mutual acquaintance, and Holmes keeps some measure of contact up with his brother. Also, not a lot of police officers seem to like him.
Mycroft Holmes is a much more standard example. Whereas Sherlock can form some close friendships and be personable when necessary, Mycroft lives alone, works alone and spends his free time at a gentleman's club where so much as acknowledging the existence of another member puts you at risk of expulsion.
C. Auguste Dupin and his anonymous narrator in the works of Edgar Allan Poe are even more isolated than Holmes and Watson although they still retain certain contacts in the police that allow them to carry out their amateur detective work.
Frankenstein's Monster. Obviously. In fact, an Alternative Character Interpretation is that Victor Frankenstein is the villain and the "monster" his victim. The monster himself points out that Victor created him and then immediately abandoned him, never allowing him to know love or affection. It poses a sort of chicken-or-egg question: is the monster a loner because he's a freak or is he a freak because he's a loner?
Victor himself was a Mad Scientist loner-freak when he was busy creating the monster, and was upset to find that when he arrived at university most of the science he studied- really what today we'd call alchemy and the occult- was deemed to be out of date, and took to trying to prove its worth on his own. He notes that he became less and less sociable while creating the monster, and tried to get over his sheer horror of what he had created by throwing himself back into human company and abandoning his research.
My God, mannie, if Freckles hadna the birds and the beasts he would be always alone. It was never meant for a human being to be so solitary. He'd get touched in the head if he hadna them to think for and to talk to.
Tobias has a lot of this after he gets trapped in morph. He does spend a lot of time with the other Animorphs, but he also has periods as a loner because he struggles with his triple hawk/human/Andalite nature and figuring out where he fits in in the world. It gets taken Up to Eleven at least twice when he retreats from everyone and sometimes even lets the hawk take over-right after he gets trapped and after Rachel's death.
Arguably, David. He moved around a lot as a human, and eventually gave up on maintaining close relationships. Could explain why he went axe-crazy in the end.
While Elena is going through Godmother training in The Fairy Godmother, it's brought up that Godmothers need a certain amount of contact with others to keep them from flipping out. This would have been averted for Sorcerers/Sorceresses, who are claimed to spend large chunks of their lives in isolated study (without going bonkers), if it weren't for the fact that the Sorceress with the most page time is Arachnia, and fixing her up with a good man was the cure for her problems.
Zahrah in Zahrah the Windseeker tends to be introverted and shy, which doesn't help her reputation for being weird since she is already dada (born with dreadlocked hair with vines in it). She faces this stereotype all the time.
Scott in Hobgoblin wants little to do with his high school peers and they want little to do with him. This also makes him a primary suspect when people start dying.
In H.P. Lovecraft's short story The Whisperer in Darkness, countryside folklore has associated the strange space monsters with the recluses around the area.
...there are shocked references to hermits and remote farmers who at some period of life appeared to have undergone a repellent mental change, and who were shunned and whispered about as mortals who had sold themselves to the strange beings. ...it seemed to be a fashion... to accuse eccentric and unpopular recluses of being allies or representatives of the abhorred things.
Christian Ozera from Vampire Academy is a spooky, slightly violent guy with a shady family and no friends who hangs out at the church. He is treated as a freak and a "Strigoi-wannabe" by his classmates.
The Secret Garden: Mary and Archibald Craven are regarded as this at the beginning. The former because she prefers to play by herself, and the latter for living alone in a huge mansion with no visitors and the doors all shut up.
In The Southern Reach Trilogy, the biologist is extremely detached from the rest of humanity and overly-focused on certain details, leading her to get fired from most of the jobs she had and she was considered a poor candidate for the expedition. Which is why the director picked her. She's so intractable and freakishly self-contained that she cannot be hypnotized and possibly caused her cloning to go wrong, resulting in Ghost Bird retaining far more individuality and memories than the other clones.
Smaller & Smaller Circles: When Jerome, Saenz, and the local authorities begin looking into the backgrounds of possible suspects, they initially dig up very little on Alex Carlos, the resident community dentist. All they know of him at first is that he is single, works efficiently and keeps to himself (even Eating Lunch Alone). He eventually confirms the investigators' suspicions.