"Yeah, I used to be but there was sort of a paradigm shift last spring."
Justified in the light novels in that he actually was alone, saying things like "Friends lower your value as a human" with a straight face. Hanekawa was the first to actually acknowledge him after he accidentally saw her panties, and they became definite friends after "the vampire incident."
For people who repeatedly say they only have friends because of the main character, the cast of Sailor Moon sure know a lot of Victims Of The Week from early childhood...
Played with in Puella Magi Madoka Magica. Madoka claims that she feels lonely at times due to thinking that she is weak and useless, but the anime clearly shows that it's all in her head as she has a loving family and caring friends.
Batman. For a guy who is torn by emotional isolation living eternally in the darkness, the guy has a ridiculous character page full of his constant allies. This is hardly even mentioning that his relationship with Robin was so close during the Silver Age that you didn't need to be part of a censor board to interpret some Ho Yay going on there.
In fact, the Bat Family is probably the largest in the DCU. There's at least currently a Batman, a Robin, a Nightwing, a Red Robin, Catwoman, Oracle, Batgirl, Black Bat, Batwoman, Flamebird, Spoiler, and Alfred in this loner's gang. Though to be fair, he does mostly work alone where feasible and leaves the others to their own devices.
For 17 years this supposed loner starred in a book whose premise was to team him up with everyone else in the DC Universe. Now with Batman Inc, (Loads and Loads of Batmen!) the writers might as well stop kidding themselves. Ever since Grant Morrison started writing Batman regularly, they have.
One Superman/Batman story parodied this when two children argued about which hero was cooler. Both agreed that neither hero had much use for the Justice League; Superman, because he's more powerful than the rest of the League combined, and Batman because he's a loner, except when he's working with his own sidekicks and the Outsiders. Even children in-universe don't buy Batman's "loner" act.
Wolverine claims to be a loner, and does honestly seem to attempt to do so, but his track record seems to prove otherwise.
To a degree it works for Wolverine; by temperament he'd be a driftingKnight ErrantIn Sour Armor, which involves lots of helping people and then leaving and not seeing them again for several decades. In a slightly different genre he'd very reasonably say But Now I Must Go. Look at that trope page; fully half the links in the description apply to him. (For example, until he regained his memories, his Journey to Find Oneself was a big part of his character.) All that being said, it becomes ridiculous to call Wolverine a loner when he is officially a member of three superhero teams at once, due to him publicity. Being a loner is in character, but the Marketing department wins, especially in a Shared Universe.
He also has had a girl sidekick following him around for most of the past thirty years. (Shadowcat, Jubilee, Armor...)
For someone always looking out for his own interests, Han Solo has what seems to be quite a close (if vitriolic) friendship with Chewie, and a whole entourage by the end of A New Hope.
Invoked in Pee-wee's Big Adventure, when Pee-wee tries to brush his would-be girlfriend off by claiming to be a loner, in spite of having hordes of friends.
Bella from Twilight spends the first two chapters whining about how no one would ever like her and how she has never had any friends. She spends every other chapter whining about how people just won't leave her alone. And from the moment she sits down in school, she starts making friends and boys start asking her out. Yes, she's clearly unpopular.
Live Action TV
Played with the title character of House. While he is often curmudgeonly and rude (particularly to patients), he also seems equally unable to function unless there's people nearby who he can make rude comments to. In episodes where he's deprived of his team, he is shown to be struggling without them. He refuses to admit this, even when he resorts to asking a janitor to help out on a differential diagnosis and dealing with families in his stead. (Who's he? Oh, uh, Dr... Buffer).
In an early episode of LOST, Kate gives Sawyer some advice, starting with the words: "from one island outcast to another..." Kate practically runs Craphole Island, and has relationships with all the major characters.
The Tenth Doctor had elements of this. He had loads of friends, allies, acquaintances, etc. who all love him dearly, but chose to wangst instead of say, stopping by for tea now and again. Lampshaded by Sarah Jane in "Journey's End":
Sarah Jane: You know, you act like such a lonely man but look at you! You've got the biggest family on Earth!
One of the Fourth Doctor's gimmicks is that he's more of a loner than the other Doctors, but in practice this is mostly demonstrated with the occasional bout of Jerkass or Stay in the Kitchen behaviour when the writers remember he's supposed to be like this, and he takes on companions just as readily as any other Doctor.
In Gilmore Girls Rory is initially portrayed as an awkward teenager who is more interested in books than people... too bad every person she meets instantly adores her and falls at her feet. (To the point she even gets elected student body president despite being a so-called geek.).
An amusing example in NCIS:LA. Paris, an agent, claims to work alone. She works with a tight-knit team whom she literally lives with in a pair of huge trucks.
In the series four finale of Merlin, Arthur goes after Merlin and tells him: "you're the only friend I've got." Except for Gwen, who's travelling with them. And Hunith, whose house he recovered from his injuries in. And the Knights of the Round Table, who are currently trying to make their way back to him. And Tristan and Isolde, both about to thrown in their lot with him. And Gaius, back in Camelot.
Charlie Brown in Peanuts goes in and out of this - everyone supposedly hates him, yet he seems to hang around with people like Linus, Lucy, and Schroeder a lot. In this case this was probably at least a little deliberate—Charlie Brown is more insecure than a loner. His insecurities just lead him to feel lonely.
And Lucy's verbal abuse can't help.
In the earliest strips, the other characters are in fact shockingly cruel to Charlie Brown. This motif is softened over time.
Raven in Rune Factory 3 tells you that she doesn't have any friends (because she is afraid that her "curse" will make them disappear). However, on every Holiday and Festival you see her walking around with Karina and Sofia.
One of her heart events will acknowledge this: She makes gifts for Karina and Sofia, thanking them for being her friends. They both express surprise this was ever in question.
In Harvest Moon: More Friends of Mineral Town, when you're introduced to Doug and Ann, Doug expresses hope that you'll be friends with his daughter, Ann, since she doesn't really have any friends and is lonely. But during the normal course of the game, you'll see her hanging out at the hot springs every morning, with Popuri. Does Popuri not count?
Hisao: To tell the truth, though, I do prefer solitude to being surrounded by others. I don't think I could maintain a social circle like you do.
Lilly: I don't think that's true either. I've seen how gentle and caring you are around Hanako, and you get along marvelously well with others, even those whom you hardly know. I think you're quite adept at social situations.
Dangeresque from Homestar Runner works alone, except when he works with Renaldo. Which is all the time.
In Wapsi Square Monica has an episode where she wonders if she is a social misfit  until she meets someone who truly doesn't have any social life, and she ends up giggling over her self. .
Davan of Something Positive is the kind of misanthrope you would expect this of... except he has a sprawling group of friends, both close and distant, which grows and changes over time. Even Mike managed to get a lot of new friends thanks to his Jerk Face Turn.
I'm a Marvel... And I'm a DC parodies this in regards to Batman in Sh*t Batman Says, in which the title character starts to make a big deal about working alone... and immediately afterwards thanks Alfred, Nightwing, Batgirl, Robin, and the Justice League for their help.
The titular character of Daria, despite appearing to be an isolated loner, is actually on good speaking relationships with most of the other characters in her class, interacting with them fairly often. Granted, she tends to do so in a fairly ironic way.
At the same time, Daria does try to avoid interacting with most of them; usually they track her down for some reason, or events force her into human interaction.