Guts, the main protagonist of Berserk, starts off as a mercenary loner struggling with his inner demons of anger and has no interest in making connections with others (and he Hates Being Touched). Throughout the series, though, he finally begins to accept his new friends in the form of the Band of the Hawk.
Koji Minamoto from Digimon Frontier was a loner at first, distancing himself from Takuya and the others when they all first arrived to the Digital World. It's not until Episode 6 that he permanently joins the group.
Tsume from Wolfs Rain. He is described as a "stereotypical angry anime loner" who withdraws himself from his allies, but despite this, he eventually grew respectful of Kiba and became a permanently loyal member of the pack.
Shido Fuyuki from Get Backers started of as a loner with the ability to talk to animals (and considered them as friends), but it took one Get-Backers member, Ginji, to make him more of a different person.
Dorulumon from Digimon Xros Wars started as a lone wolf and a former member of the Bagra Army. At first, he refused to be a part of the Xros Heart, but as soon as Tactimon tells him about his past, he changed his mind.
Naruto himself counts, since he was a loner in the years before the series began. In fact, part of the reason why Naruto and Sasuke became friends is because both of them understood what it was like to be truly alone.
Kiyo Takamine from Zatch Bell! begins as an introverted loner due to being picked on by others and started skipping school, but that all changed when Zatch's influence made him more of a sociable person. Thus, the two are officially friends.
Mikagami Tokiya from Flame of Recca begins as an revenge-driven loner with a cold attitude towards everyone except Yanagi, who was the reason he warmed up a bit, and he later became an official member of Team Hokage.
This happens a bajillion times after that, with Yuma typically dueling a character with even worse social skills than him, and inspiring that duelist to be his friend, and nicer in general.
Barnaby Brooks Jr. from Tiger & Bunny. Even though he's somewhat of an nice guy, he's too introverted to be interested in making any intimate relationships, but thirteen episodes later, him and Kotetsu are now Heterosexual Life-Partners.
Captain Gundam from SD Gundam Force was a loner rebuffing companionship from Shute, but he realizes that The Power of Friendship was the very thing to activate the Soul Drive. Thus, Captain officially accepted Shute as a friend.
From One Piece, Tony Tony Chopper was an outcast due to his weirdness in character, but that all changed when Luffy and the others accept him into his crew.
Brook also qualifies, as he spent fifty years alone before meeting up with the Straw Hats. Despite being a bit more sociable than others on this list, this did cause him to spend much of his introductory arc fighting alone, rather than endanger Luffy and the others by asking for their help.
Robin as well, who spent twenty years on the run from virtually everyone in the world and betraying others in order to survive. It took a lot of effort on the parts of the Straw Hats, but now she cares very deeply for them all.
Rozen Maiden: Jun started as a Hikikomori because he was rejected by his peers for his interest in sewing, which made him very depressed. Thanks to Shinku, he finally comes out of his shell and is close with her and the other crazy dolls.
Fakir from Princess Tutu started off as an Ineffectual Loner for almost the entire first season, but decided to (reluctantly) team up with Ahiru from then on, although another season later, he still has the tendency to revert back to do things by himself.
Uryu Ishida from Bleach was more of an intelligent loner and an Insufferable Genius to boot. While he will deny being friends with Ichigo, he becomes an frequent ally to him and the other Soul Reapers, only when their goals are the same.
Shin of Eyeshield 21 was a loner with No Social Skills until he joined the football team in middle school, making this development show it was through football that he was able to make friends.
Yukiteru Amano from Mirai Nikki started as a loner in school due to his anti-social personality, but he does try to get better in making friends. Unfortunately for him, Yuno doesn't want anyone closer to him. Eventually he manages to make a small group of friends with his classmates, but later on he kills his friends in his quest for Godhood. He was a freaky loner who got better, but it was too late for entirely other reasons.
From Full Metal Panic!, Sagara Sousuke was a loner avoiding others due to following business-related orders, but this didn't stop him from ending up with a group of True Companions.
Mizuki from Kamisama Kiss. He has been alone tending to abandoned shrine for decades when Nanami meets him and by that time he is ready to change his situation a bit. Unfortunately, the way he goes about doing so nearly winds up getting him killed by Nanami's Battle Butler, Tomoe.
Alan: You guys might not know this, but I consider myself a bit of a loner. I tend to think of myself as a one-man wolf pack. But when my sister brought Doug home, I knew he was one of my own. And my wolf pack... it grew by one. So there... there were two of us in the wolf pack... I was alone first in the pack, and then Doug joined in later. And six months ago, when Doug introduced me to you guys, I thought, "Wait a second, could it be?" And now I know for sure, I just added two more guys to my wolf pack. Four of us wolves, running around the desert together, in Las Vegas, looking for strippers and cocaine. So tonight, I make a toast!
The film Henry Poole Is Here deals with the main protagonist moving back into his old neighborhood, spending time alone suffering a disease which will eventually take his life. Thanks to a nosy neighbor, Henry begins to accept the help from others which cured his disease and changes his perception of life.
Toklo from Seeker Bears started off as a loner due to being rejected by his mother and was bitter because of it, but as the journey progresses, he accepts the other bears as his friends.
Harry Dresden of The Dresden Files. In the first few books, he started off as a loner, but a few books later, he formed some bonds with other characters like Murphy, Thomas, a couple of Knights of the Cross, and so forth.
In The Lord of the Rings, Aragorn is such a character, being a ranger. He joins Frodo and Sam in order to protect them.
Tomoko Nozama from Kamen Rider Fourze. She's a quiet Goth who choses to be a loner, although she is hiding her true feelings. Thanks to Gentaro, she's becomes the seventh member of the Kamen Rider Club and graduated to a permanent Perky Goth.
On Happy Days, Fonzie was originally a loner who the other guys looked up to and occasionally consulted for adivce, before becoming a Breakout Character and moving in to the Cunninghams' garage apartment.
Rob from Ghostwriter first appears a loner that the team suspects in a case. Although he's a bit resistant at first, he ends up becoming their friend and joining the team after Ghostwriter revealed himself to him.
Dr. Cox from Scrubs was considered a loner in the very first episode, but it wasn't until the second where he started to hang out with the rest of the crew more often.
Reginald Barclay from Star Trek: The Next Generation was seen as quite a loner in his first appearance. He surrounds himself with recreation of the other crew members in the Holo-Deck, but he soon becomes less like one as he gains the groups' respect and deletes the Holo-Deck versions.
Karen McCluskey from Desperate Housewives was a rather bitter loner who initially served as Lynette Scavo's Sitcom Arch-Nemesis until it was revealed that her bad attitude stems from her son's untimely death. The two become good friends after Lynette helped Karen when she was suffering arthritis.
This is part of Simon Bellamy's major Character Development from Misfits. He started as a quiet and socially-inept loner suffering from years of mistreatment and isolation, despite being a really nice guy who desperately desires for friends. After that, he becomes more of a confident member of the group.
Angel was a loner during his backstory, due to his guilt and not wanting to risk attacking anyone. He came out of it for most of the series, though he sank back into it in season 2 in an attempt to protect everyone from his darkness like before.
Knuckles from the Sonic the Hedgehog series lives a solitary life born with a task to guard the Master Emerald in Angel Island, but became a trusted ally and friendly rival to Sonic.
Blaze from the Sonic Rush Series is another example. It took the first game for her to learn how to accept help from others and make friends. Although she's still a loner who has to guard the Sol Emeralds in her alternate dimension, she still assists Sonic and the gang.
In Disgaea 3: Absence of Justice, Mao spends the entire game as the Ineffectual Loner caring about his goal to defeat his father to become a hero and has the tendency to disregard the needs of others. During the course of the story, however, he begins to warm up to others and more or less sees them friends, although he will never openly admit it.
The World Ends with You: Neku Sakuraba started off as both a loner and a selfish Jerkass, but over the course of three weeks, he eventually learns of the value of friendship. In the Reapers' Game if he doesn't cooperate with others, he will get erased.
Squall Leonhart of Final Fantasy VIII started as the anti-social protagonist loner who throughout the course of the game developed friendships and has hidden feelings for Rinoa.
Amarant Coral of Final Fantasy IX was initially a loner who works as a bounty hunter living by the honor code of "only the strong survive". While he was the last character to join Zidane, he was still dismissive of The Power of Friendship, but that didn't last long when Zidane saved him from falling into his death, which is what changed his heart.
Herschel Biggs from L.A. Noire was rather reluctant about being assigned partners, especially with Cole Phelps, and he would rather get the job done by himself. In the end, he does warm up and accept Cole.
The essence of the Fire Emblem series. Most of your party is composed of loners that you pick up throughout the game.
Downplayed with Wrex in Mass Effect 1. He's a mercenary who prefers working alone to being in a large army, but Shepard's squad is small enough that he doesn't mind working with him/her. Thanks in large part to Shepard's influence, Wrex goes from a burned-out mercenary in Mass Effect 1 to chief of the Urdnot clan and de facto leader of the krogan in Mass Effect 2 and 3. In the second game, Wrex's reaction to meeting Shepard again is to immediately stop what he's doing, exclaim "Shepard! My friend!" and hug him/her. The third game also reveals that he's friends with Liara and Vitriolic Best Buds with Garrus.
Liara in the first game is a shy, awkward bookworm who prefers working alone in archaeological digs to being with people. She matures throughout the trilogy, befriending most of the squad and being a potential Love Interest for Shepard, but ultimately still prefers working with data to socializing.
Token Evil Teammate Jack from the second game is a loner as a result of being tortured and a child and being betrayed by every person she ever trusted as an adult. Once again, as well as being a potential Love Interest for male Shepard, being on Shepard's team changes her so much that, if she survives the second game's Suicide Mission, she's become a teacher by Mass Effect 3.
Justicar Samara from the second game is married to her job, having given up all of her worldly possessions and personal relationships in her quest for justice. She still becomes close to Paragon Shepard, and, while she's a Not Love Interest, she tells him/her that in another world, where she weren't a justicar, she would definitely want a relationship with Shepard. (Renegade Shepard...not so much.)
Mass Effect 2's Legion is a strange example. Being a Mind Hive robot comprised of 1,138 separate programs, and with the capability to connect to the larger geth collective, it's never truly alone. But, because it's a geth platform, it's distrusted by nearly all organic life (the hole in its chest? A colonist on Eden Prime shot at it with a rifle). As the third game confirms, Shepard is the first organic in over 300 years to actually interact with a geth for a purpose other than killing it. Even Tali, a quarian (who were driven off of their homeworld by the geth during the Morning War), considers Legion to be a friend by the third game.
Javik from Mass Effect 3 is an extreme example. He's the last living Prothean (having been in stasis for the past 50,000 years), and, as the Protheans' avatar of Vengeance, is focused on nothing except stopping the Reapers. Still, he obviously respects Shepard and becomes much more amicable throughout the game. If you discourage him from reliving the memories in the Echo Shard, before the final battle, he tells Shepard that, after the war is over, he's going to help Liara write her book on Prothean culture.
Valkyria Chronicles: MarinaWulfstan is portrayed as a loner in both the game, and the anime adaptation. She even gains a skill called 'Lone Wolf', which acts as a double edged sword: it increases her accuracy the further she is from your other units. At optimal distance, it guarantees 1HK's. But it also causes her accuracy to suffer greatly, when near others.
Sunstone has Allen, who back in collage was so cynical towards other people's attitudes towards his BDSM interests it took a while for him to realise Ally was actually being friendly. So much so that Ally had to resort to strong measures to get his attention and show him she had no reason to further the slander against him. Ever since? BFFs.
Cera from The Land Before Time became this to Littlefoot in the first movie, although she still has the tendency to do things on her own due to her disagreements with him and the others in the later movies.
Although he was a minor character and only appeared in one episode, Mike Believe from The Powerpuff Girls is somewhat an example of this. He starts off as a loner with an Imaginary Friend who later caused trouble in the kindergarten class. After the girls defeated the evil imaginary friend with an imaginary friend of their own, Mike explains to them that he just wanted to have friends, so the girls accepted him as a friend.
At the very start of My Little Pony: Friendship Is Magic, Twilight Sparkle is focused on her studies to the exclusion of nearly all social interaction. When Nightmare Moon usurps the throne and threatens to plunge Equestria into eternal night, Twilight tries to find the artifacts necessary to stop Nightmare all by her lonesome, but five other ponies insist on helping her. By the end of the second episode, Twilight realizes the six of them have become Fire-Forged Friends, and this epiphany proves necessary to defeat Nightmare Moon. From this point forward, Twilight becomes a firm believer in the Magic of Friendship, although her lack of prior social interactions later leads to some awkwardness between her and her new friends.
Zecora lives all alone in the Everfree Forest for reasons unknown to the viewer, but she didn't make an active effort to be alone when she went to Ponyville. The residents were so afraid of her that they would hide when she went to the town. When the members of the Mane Cast get to know her, they find she's actually a very nice zebra and they become friends, going to her on many occasions when they need help with magical issues.
Darkwing Duck: The titular character started as a loner for dismissive of assistance from Launchpad and Gosalyn in the two-part pilot episode, but later on accepts the two as friends, despite still having the tendency to do things on his own again.
The Ice King from Adventure Time was a bit of a loner due to him being ruler of Ice Kingdom, which is uninhabited despite having ice creatures to keep himself company. He soon warms up when he makes friends with Finn and Jake.
Ed, Edd n Eddy: The three main characters serve as outcasts trying to fit in with the other kids, who seem to mistrust and mistreat them a lot (although Eddy gets this treatment the most and not the other two Eds). In the end of Ed, Edd n Eddy's Big Picture Show, however, the kids finally accepted the boys as their friends after realizing how cruel Eddy's brother was.
Wheeljack from Transformers Prime started off as a bit of a lone wolf who claimed to prefer being on the move rather than being tied down to any one place. While he fought well by himself and alongside Team Prime, he continued to gently rebuff their offers to be a more integral member of the team. He later claimed to prefer being by himself. Arcee however caught him in his lie and he eventually admitted that he just wasn't completely comfortable with change. Eventually, he joins Team Prime