Rin Okumura. He's Book Dumb, somewhat kluzy at times, goes all awkward when it comes to girls he likes, is very childish - especially with friends - and is an AMAZING cook. This◊ popular image says it all.
Konekomaru is shy, shortglasses-wearing smart guy who adores cats.
Shiami Moriyama is downright adorable, so darned sweet, as well as terribly awkward around people.
Digimon Adventure 02 has Davis/Daisuke who is such a ditzy goofball and can be rather silly around his crush. One of the dorkiest things to behold, yet OH SO CUTE!
Jean from Nadia: The Secret of Blue Water. Not only is he intelligent, he is also generous, sweet-natured, caring, friendly, loyal, naive, and dedicated to what he likes. He's quite brave, as well. Of course he's naturally green when it comes to social graces around the opposite sex, but in a way it proves to be an asset. Nadia's English voice actress once said that she would date someone like him "in a heartbeat".
Yugi Mutou, the actual one, not the Super-Powered Evil Side. He's a slightly dopey, socially awkward kid whose deepest wish in the first chapter is just to have a few friends. He gets them though, because people finally start seeing and appreciating his Incorruptible Pure Pureness.
Ryo Bakura also qualifies, if he isn't more so. He's the shy kid in the sweater who's obsessed with games of all kinds and has very little friends. Too bad he was downplayed in the anime. And again, this is the REAL Bakura we're talking about. The Spirit inside him is...less adorkable.
Team Taiyou, also from 5D's. Most of the WRGP finalists are elite duelists with expert decks and strategies, and have the attitude to go with them. Taiyou, on the other hand, are just a couple of poor, friendly guys from the country who eagerly want to prove their worth to the world. The hijinks that ensue when they try to put together a bike and deck are hilariously endearing.
Keitaro in Love Hina. Sure he might be a huge Accidental Pervert, but his genuine desire to know the other tenants and his constant determination are endearing.
Yomiko Readman in Read or Die. The quintessential bookworm. So nerdy. So cute. And so very, very scary.
Rukia has had her moments: her love for cute things and bunnies-specifically chappy, not to mention her drawing skills (or lack there of), plus her "innocent (and dramatic) girly schoolgirl" act she puts on in front of Ichigo's family and classmates is too adorable.
Naruto. When he's not in Determinator mode he's socially awkward, and early on, most of his boasts came off more as cute/laughable than intimidating. Not to mention Hinata and Rock Lee.
No one could have predicted that Hashirama, the First Hokage, was this. He noticeably stands out against his brother, the Second Hokage who is very stoic while the former is goofy, friendly and just plain Keet, cheerfully admitting he spoiled his granddaughter rotten. One person even commented how it was hard to believe that such a cheerful, happy-go-lucky person used to be one of the strongest shinobi in the world. Proves to be a Crouching Moron, Hidden Badassby intimidating his brother, Sasuke, Juugo, Suigetsu, and Orochimaru through sheer willpower without moving an inch.
This is about half the point of "Li Sheng Shun" in Darker Than Black. He's so adorably inept, clumsy, kindhearted, and naive that you just want to hug him, and nobody would ever suspect he's secretly the Black Reaper, the most badass and stoic guy in a series full of emotionless killing machines.
Edward Elric , especially when dealing with anything related to Winry and romance and his adorable overreactions over his height and anger at being called "little" brother.
Josuke, from Part 8 of JoJo's Bizarre Adventure. Obsession with measurements? Check. Strange habits such as sleeping under the mattress because the weight of the mattress makes him comfortable? Check. High intellect? Check. An abysmal grasp of common sense caused by the fact that he hasn't any memory? Checkmate.
Gourry Gabriev from Slayers is often viewed as adorkable by fangirls. He's a badass swordsman, but his terrible memory (at least in the anime) and tendency to be really sweet and a genuinely nice guy make him totally Adorkable. Less so in the original novels; Gourry's actually got a bit of a dry, snarky sense of humor and he's more observant that Lina gives him credit for. Gourry's anime portrayal seems to be a Flanderization of how Lina perceives him; viz. as nonmagical as it's possible to get and therefore a complete moron.
John Brown of Ghost Hunt has his moments. Bring him up to any of his fans and the word 'cute' will come up, usually because of his charmingly naive personality and/or amusing facial expressions.
Son Gohan, especially as a teenager. He's such a sweet, friendly, good-natured guy, yet also very studious, and he gets into many embarrassing social situations, and he has questionable taste in fashion and, er, superhero poses.
Yamcha was adorkable during his teenage years but he grew out of it a little as he got older. Yamcha was afraid of girls and super awkward around them when he was a teenager, even though his dream was to fall in love and get married. He even wanted to use the Dragon Balls to make it so he would not have panic attacks around girls anymore.
Kid/Teen Chi-Chi (the former moreso), because of her massive crush on Goku and her constant blushing and crying. You can't help finding her Adorkable.
Goten. Gohan's friendly, good-natured hyperactive brother. His innocence and childish personality is what makes him adorkable.
Goku. Huge goofball with a high voice. Having to grow up by himself, isolated from a lot of the world, he was very childish and adorably curious and oblivious to a lot of things as a child, such as love, or even what girls were like. And even though he wisened up as an adult, he still retained a lot of his adorably goofiness and childishness.
Ash Ketchum from the Pokémon anime, at least in the older seasons. He was rather klutzy and somewhat dim-witted, but also a really sweet kid with an enormous heart, and already a pint-sized Bishōnen to begin with.
Team Rocket's Jessie, James, and Meowth. Jessie for being a vain but lovable diva, James for just being so precocious and Meowth cause he's a frickin' talking cat with a New York accent! They serve as the villains but are just so gimmicky and so... fail that they aren't even threatening anymore. Their determination is admirable too.
May for being brave, optimistic, kind, and sometimes awkward.
Tamaki in Ouran High School Host Club. He has the handsome bishie looks and is very adept at flirting with girls he doesn't much know, but around friends (not to mention his actual love interest) he becomes a lot more of a lovable idiot.
Lampshaded in Tiger & Bunny — Agnes points out that Sky High's dorkiness is part of the reason he's so damn popular, with his silly catchphrase ("Thank you! And again, thank you!") among other things.
Conan himself. In the beginning of the series the only clothes he's seen wearing are his miniature suit, complete with a bow tie. This combined with his cute ways of expressing his feelings and his Sherlock Holmes obsession create top quality Adorkable material. He can also be classified as an out-and-out mystery geek, not just a Holmes geek.
Conan's dad, Yusaku Kudo. He's a mystery writer who gets a bit too excited about mysteries. Also, his glasses rock. And his wife/Conan's mom Yukiko mixes this with One of the Kids, Tsundere, and being really damn pretty.
Pointed out in Bunny Drop, where Daikichi notes how unfair it is that "Michan" (the dad of one of Rin's classmates) is also extremely clumsy. It was like he was scientifically designed to be as attractive as possible, and the clumsiness just makes him more adorable.
Suzaku (especially when he's around cats), Lelouch (especially when he's around Shirley), Rolo (around his beloved brother Lelouch), and Shirley from Code Geass.
The titular Sailor Moon AKA Usagi Tsukino, the ditzy, clumsy, yet sweet leader of the senshi.
Ami Mizuno/Sailor Mercury. She is a nerdy Cute Bookworm after all, other than an insecure Shrinking Violet who tends to have a difficult time making new friends, despite being humble and gentle.
Minako Aino/Sailor Venus at times. Like Usagi she's a bit of a ditz (also a Malaproper in the anime), and an overall perky yet lovable, cheerful and fun-loving girl.
Tsukasa from Lucky Star. She's prone to oversleeping, isn't very good at studying, and overall makes a lot of adorable mess-ups, looking just as adorable trying (unsuccessfully) to correct these faults.
Kaori Senoo from Tsuruga, a timid and socially awkward girl, who also doesn't know much about mahjong (for example, calling out riichi without getting the stick, and not realizing when she has a Yakuman hand). Her character selection screen in the PSP game lampshades this trope.
"Somehow the sight of this timid second-year student fidgeting away is just too captivating."
Kare Kano: Yukino Miyazawa is a gifted high school student lauded by classmates and teachers. This apparent brilliance, however, is mainly used as a means to garner praise. At home, Yukino is very dorky.
Watanuki from ×××HOLiC at least before Yuko's death. The way he expresses himself tend to be overly exaggerated as well as hilarious, making him even funnier as well as cute. The adorkableness adds even more with Todd Haberkorn playing him in the English dub.
Max Sterling from Robotech. Long hair, glasses, an always-friendly disposition, and his excellence with video games helping him also become The Ace fighter pilot (it's unclear whether being an Ace made him good at Veritech games or vice versa, however). That he's also voiced by master-Adorkable voice actor Cam Clarke helps.
Gerald Frolio from Bokura no Kiseki. He's an awkward and sort of nerdy priest, who clearly has something of a crush of his country's Princess Veronica. This applies to his reincarnation from the series' present timeline, Midou, to a certain extent as well.
Mei the goat from Arashi No Yoru Ni. He is a sweet little goat who's just so darn dorky and clumsy that he steals the spotlight from Gabu most of the time.
Kengo from Monochrome Factor has this in spades. Not only is he a sweet lovable idiot who bounces back nearly all the time even though he keeps getting treated as the punching bag of the group, he looks the cutest when he's crying or smiling (which is nearly all the time). too bad he gets killed off gruesomely. even worse, he went out with a smile, accepting his own death for the sake of his friends.
Free!: Rei is book smart and serious, but still does ridiculous things as if they were normal, like trying on silly patterned swimsuits with gusto, calling Rin "Rin-chan-san" note since Nagisa calls him "Rin-chan", and pretending to be a detective and making sound effects while spying on Rin.
Akatsuki, from Log Horizon, roleplays being a ninja constantly, has trouble conversing with other people, but is very earnest, so when she speaks, what comes out is sometimes very awkward.