There's been plenty of fan gushing at how cute the geeky Hiccup is. This should really be expected when he's voiced by Jay Baruchel.
Toothless, "The Offspring of Lightning and Death", is also one of the biggest dorks, and nowhere does he prove it more than when he starts courting the Light Fury in the third movie.
Astrid can be a bit of an endearing dork when acting playful with Hiccup. Her adorkable side also came forth in Gift of the Night Fury when she tried different methods to bring in the holiday spirits.
Fishlegs is quite similar to Hiccup. He's a huge Lovable Nerd who likes to spout random dragon facts.
After the final battle, Hiccup has but a few moments of remorse upon waking to find that he's lost his left foot and been given a metal replacement. But forget angst—there are dragons outside and they are now a part of the Viking village! There's also the fact that he lost his foot in battle like a real Viking — which he had wished for all his life before befriending Toothless. Finally, he gets a big kiss from Astrid meaning he has the local Action Girl as his girlfriend.
There's also the fact that Hiccup just lets 15 years of abuse from his tribe slide off without any resentment towards them.
Base-Breaking Character: Stoick. The. Vast. To a good portion of the fanbase, he counts as an Abusive Parent due to his tough words to Hiccup in the movie, and occasionally in the show. To another portion, he represents Parents as People who has to balance his job as chief and father.
Crossover Ship: Due to how both films were released in the same year, there's a fair amount of Hiccup/Rapunzel.
Fanon: While Snotlout was Hiccup's cousin in the books, no such relations are ever mentioned in the films and animated series, the Haddock and the Jorgensons being portrayed more as Feuding Families than competing branches of the same clan. Regardless, fans and fanfiction still see them as cousins, with a lot of Snotlout's attitude towards Hiccup being based around his position as heir to the chiefdom.
First Installment Wins: Though the other two movies have their fans, both are also contentious for different reasons, like the Big Bad Drago being a Flat Character, several characters being underutilized and a poor tone balance in the case of the former and a highly divisive ending for the latter. As a result, there are plenty of fans who prefer the first movie for its charm and lacking said contentious elements, and this is reflected in its 99% rating on Rotten Tomatoes compared to the sequels' lesser (albeit still high) 92% and 91% respective ratings.
There's also a fair similarity plot-wise: an outcast child bullied by others in their community befriends a powerful, dangerous creature feared by all, managing to uncover a good and gentle side in the creature. Both the franchises' TV series adaptations also have similarities in the episodic Gotta Catch 'Em All narrative, with the main protagonists trying to rescue experiments/dragons and learn how to use their unique abilities for good.
One True Pairing: Hiccstrid. Holy shit, is it sacred to the fanbase (just take a look at the comments on this video). Interestingly, it only became this after the TV show and the sequel came out, with many agreeing that the "romance" in the first film was tacked-on and lacking in depth.
Self-Fanservice: Thanks to her Ensemble Dark Horse position, Ruffnut gets a lot of this. In canon, she's honestly not particularly pretty, largely because she looks a lot like her Half Identical Twin brother Tuffnut (who isn't particularly androgynous either). But just wait until you see how the fans draw her...
Signature Scene: The "Forbidden Friendship" scene where Hiccup and Toothless bond and the "Test Drive" scene where they have their first full flight over the sea are often cited as the most memorable, iconic moments in the entire franchise.
They Changed It, Now It Sucks!: The creators of the Arena Spectacular decided to go for an emphasis on realism when designing the animatronics, as the Walking With Dinosaurs Arena Spectacular had before it. Unfortunately, this misses the point of the designs (where the Dinosaurs franchise is known for its realistic CGI constructs, Dragons is known for its memorably cartoony and exaggerated designs.) This attempt brought the dragons straight into the Unintentional Uncanny Valley, with Toothless going from an adorable lizard-panther into something that can best be described as a nightmarish bat-toad.◊
The Terrible Terrors remind one of hyperactive, firebreathing chihuahuas. Enter the awwwww factor when one of them snuggles under Hiccup's arm and purrs itself to sleep there. A bit of trivia: That particular Terror was voiced by Paco the Chihuahua, after sound designer Nia Hansen of Skywalker Sound saw a video of him on YouTube and paid his owners $100 for Paco's voice: video 1, video 2, local news articlearticle 2.
Gronckles, especially the one Hiccup tames with the dragon-nip.
Viewer Gender Confusion: Quite a number of viewers thought that Toothless was a girl when he first appeared. Unintentional feminine symbolism shows up around Toothless throughout the first film, such as Toothless looking at a bird's nest with eggs in it and holding onto an unconscious Hiccup like a dog or cat would cradle a newborn puppy or kitten.
The Woobie: Hiccup. Before Toothless, he's friendless, motherless, viewed as huge disappointment by his dad, bullied by his peers, ostracized by the rest of Berk and a failure at everything Viking society values.
Toothless for losing his tailfin and ability to fly, and possibly being the The Last of His Kind. (Or at least the only Night Fury among all the other dragons.)
Woolseyism: Swedish dub: The word "hiccup" is directly translated to "Hicka" in Swedish, but since and "a" at the end would be the feminine form if used on a person (male names with an "a" at the end exists in Sweden, they're just very rare), they went for "Hicke", which would be the masculine form (pronounced "Hic-KAY").
YMMV for the book series:
Angst? What Angst?: Hiccup once a book nearly gets murdered, eaten, drowned, and at worst gets nightmares later in life as an old man. He remains chipper about triumphing over ordinary Viking life, at least until Book 9.
Then subverted in Book 12, where Hiccup from the trauma loses his memory.
Broken Base: Most of the fanbase agrees that Snotlout has a Dying Moment of Awesome, but not everyone agrees whether or not said moment redeemed for all of Snotlout's horrible actions, including his multiple attempts on Hiccup's life.
Camicazi, for being a Badass Adorable, taking on several grown swordsmen on her own, and acknowledging that Hiccup is "not bad for being a boy". Some fans wish she had been added to the movie.
People also like Thuggory, the only sane Viking teen who isn't Fishlegs from another land — the Meathead Island — who admires Hiccup's ability to talk to a murderous Green Death and rallies the other boys to go with Hiccup's plan. Then he takes the Slavemark to support Hiccup and his friends follow.
Eggingarde has a following for being a Creepy Child that is scared of a monster in the Slavelands that she doesn't like to talk about because "it's bad for morale". She creeps out Hiccup and the reader with the tale he wheedles out of her about Fishlegs.
Evil Is Sexy: Alvin before he lost his hair got this treatment in-universe. He was quite a charming with the ladies apparently.
In Book One, Valhallarama punches Hiccup affectionately to show how happy she is that he is alive. The ensuing books reveal that because she is a Missing Mom that she and Hiccup have a strained relationship; it comes to a head during Hiccup's Disney Death in Book Twelve, and Valhallarama can't even avenge her supposedly dead son on the Island of Tomorrow.
In Book One as well, the Hairy Scary Librarian becomes irritated when Gobber reveals that he's stolen a library book many years ago. Come Book Six, we learn that Hairy kills any book thief on sight in the library if they don't put their plunders back on the shelf.
Any mention of Grimbeard The Ghastly, as well as his son Hiccup Horrendous Haddock II, Hiccup III's ancestor, after Hiccup learns their tale in Book 8.
The Dragon Whisperer's Way in the library. We soon learn why Grimbeard closed the library down after losing his temper at the Wodensfang, and then at his son Hiccup II.
Grimbeard's last letter, regretting how "treasure" tore his tribe apart, hence why he hid it. In How To Break a Dragon's Heart we learn thanks to the witch that Grimbeard also allowed a jealous son named Thugheart tear his tribe apart because of envy for Hiccup II, and murdered another son thinking Hiccup II was a traitor.
In Book Three, Hiccup while a Roman prisoner waits for a week for his father to come rescue him because as far as he can see escape is hopeless and he hopes his father loves him enough to find him. Stoick arrives with the Bog Burglars chasing him, right after Hiccup has rescued himself, Fishlegs, Toothless and Camicazi. In a Book Twelve flashback, long before he met Toothless, Hiccup wrote a plea letter to his mother while a prisoner in the Murderous Mountains, and she wrote, "You are a hero. Rescue yourself."
Iron Woobie: Valhallarama of the White Arms in How to Betray A Dragon's Hero.
Snotlout for some in book 11, when we see him lose everything and realizing that even if he kills Hiccup, no one will follow him. Hiccup, despite injured and at swordpoint, convinces Snotlout to drop the sword and join him instead.
Love to Hate: Alvin and his mother the witch Excellinor. They are the villains, but boy are they clever.
Norbert The Nutjob, despite his crazy nature, stands out as one of Hiccup's smartest human foes. First introduced in the 4th book, Norbert showcases his relentlessness as he pursues the heroes down the ski slopes. With the Doomfang leaving Hysteria, Norbert allows Hiccup and his friends to leave as a sign of gratitude, despite the trouble Hiccup had caused. Striking a deal with Madguts, Norbert had him capture Hiccup with his dragons while providing Madguts a means to get revenge against the Hooligan tribe for his ancestor. Norbert's goal is a journey to America across the ocean, where he has taken numerous precautions against threats. Despite wanting Hiccup dead, Norbert shows major restraint as he know that without Hiccup, the journey would be doomed. Seemingly killed off by the end of the 7th book, Norbert briefly appears in the finale, showing that he's now once a part of the tribe he had enslaved, yet accepted him and sees Hiccup as the one who should be King of the Wildewest.
The Scrappy: Snotlout eventually earns this status in-universe after he betrays Hiccup one time too many.
They Wasted a Perfectly Good Character: The Haddock family tree reveals that Snotlout Jorgenson has a sister named Adelaide, but she never actually appears in the story. It's not known if she's an older sister, or a younger one, if she's questing during the series or not even born, given Baggybum might have conceived another child after Snotlout dies with the need for an heir. We also don't know the relationship she and Hiccup have with Hiccup and Snotlout being Cain and Abel.
Toy Ship: Camicazi and Hiccup are usually shipped together, since they can be Back-to-Back Badasses and get along well.
The Hairy Scary Librarian. Sure, he is Ax-Crazy and hoarding all the books in the library for himself and killing anyone who tries to steal said books, but he gives the thieves fair warning to return the books before he slices them up, and gets sent to the Amber Slavelands because Hiccup frames him for stealing a Murderous Stealth Dragon. And when the witch lies to him about receiving freedom, he switches sides quite easily after settling his score with Hiccup.
Furious as well. With the Trauma Conga Line that ensued after he lost his older brother Hiccup II, Hiccup III's ancestor, you can't blame him for believing that Humans Are Bastards. While he doesn't hate Hiccup III personally, he doesn't want dragons to become slaves again or destroyed by the Dragon Jewel, and in his future vision he sees that Hiccup will become the Mike Nelson, Destroyer of Worlds for dragons.
Unintentionally Unsympathetic: Grimbeard the Ghastly, Hiccup's ancestor. It's hard to feel compassion for a guy that had no qualms about enslaving the dragons and people alike after the Wodensfang tried to talk sense into him, abandoning his infant son for being a runt and stealing him from his Mama Bear wife, allowing his wife to wander into the wilderness and presumably die of starvation, and then kill said son when the latter was trying to hold a peaceful protest for enslaved dragons. Then instead of fixing the mess he created, he banished the living son that he knew was a traitor, leaving an idiot heir on the throne, and rode off into the sunset after setting booby traps for his treasure and Lost Things He dug his own grave the minute that he wouldn't take the Dragonmark.
You've got Hiccup himself, who has to undergo a huge Trauma Conga Line to become the Last Great viking Hero.
His ancestor Hiccup II also has to count, given he has a Shoot the Shaggy Dog story and quite a traumatic childhood.
His friend Fishlegs who is an asthmatic orphan and fellow runt; when he tries to find his ancestors on the island of Berserk, the Berserkers laugh at him.
Stoick the Vast is also a bigger Woobie here than he is in the movies because he is Dumb Muscle who loves his son and does the best that he can as a (mostly) single parent, chief, while not comprehending that the world needs to change and that change has a price. Not to mention that with his son nearly dying once a book.