River Tam of Firefly owes her popularity to this trope. She's played by the gorgeous Summer Glau who can pull off cute teenage looks very well, and River can kill people with her brain or use mathematics to shoot several very tough soldiers.
Cameron: (lifting a young boy off of the ground) If you call your mother, the man will use her to get to you. He will kill her, then he will kill you. Sarah: (sternly) Cameron. Cameron: ... Would you like a bedtime story?
Carter, Genius Ditz of Hogan's Heroes, is usually innocent, oblivious and acts far below his years. He's also a complete fanatic about his bombs and has probably directly killed more people than anyone else in the group.
Tamara Adama from Caprica appears to be shaping up into one of these - rather quickly as well. Might also be a Little Miss Badass.
Hiro. The man tends to evoke feelings normally reserved for small puppies and kittens (being played by Masi Oka really helps) and is a Wide-Eyed Idealist in a world full of cynics, but do not underestimate him. That sword is very much a weapon, and he can and will use it if he needs to - as Sylar found out. As long as you're not trying to nuke New York or otherwise destroy the world, though, he's more than happy to just eat his waffles.
Vala Mal Doran wears her hair in pigtails, she's been seen by anyone passing by the SGC halls in a bathrobe with curlers in, she eats... enthusiastically, she's jumped on Teal'c and hugged him (she only doesn't do that to Carter, it seems, because Carter's not 6'3 and built like Teal'c. Sure, a tall and strong woman - there's a essay on that somewhere, about fanfic writers and their notions of male-female relationships - but maybe not that prepared for a full Vala hug). Anyway, yeah, she can kick your butt shooting cans while Mitchell complains about Kansas cell reception, she was convincing (if merciful) when she pretended to be a Kull warrior, and she doesn't let torture or being burned alive distract her from pulling her weight. Amnesiac and hunted by people who want to mind-frell her, she survives very well and full-memory Cam comes out worse than she does.
Bunny Ears Forensic Technician Abby Sciuto typically bounces between Hot Scientist and Moe. Until you threaten her or someone she cares about; at which point, she'll thoroughly kick your ass, and be totally adorable while doing it. And kill you without leaving a single shred of forensic evidence!!
Zach, the son of a man who is kidnapped because of his knowledge. He has an incredibly good memory, and when the men that kidnapped his father try to kidnap him, Zach punches him in the 'nads. Abby nicknames him "Mini-Gibbs".
The show has Anna. Cute, bookish and a badass vampire.
Caroline. After what she did in "Killed or be Killed", beating up Mason Lockwood and rescuing Damon, Stefan and Elena, and preventing Tyler Lockwood from killing innocent people when he first changed into a werewolf in 'By the Light of the Moon', Caroline is definitely a Badass.
Glee: Becky Jackson wants chocolate, or she will cut you. Don't mess with her. She's the only person in the school Sue Sylvester considers worthy of Dragon status.
Sherlock has Dr. John Watson. He's played by Martin Freeman, wears cuddly jumpers, types with one finger from each hand, and spends most of the series being the most caring friend in the world. He's also an ex-soldier, shot a bad guy in the shoulder in one building....from the other building, has stared down the most dangerous man in England, Mycroft Holmes, and was prepared to do a Taking You with Me to the most psychotic one Jim Moriarty. He also punched a police chief, breaking his nose and earning himself an arrest, because the guy called his best friend a "weirdo".
Pulled off by actor Jamie Bamber on Law & Order: UK, where his character's (Matt Devlin) stunning good looks and charming demeanor tended to make witnesses easily trust him and suspects underestimate him, leaving them thrown for a loop when his badass side comes out.
Community: Annie. When she is playing paintball or when she needs to chloroform a man twice her size. Twice her size. Or cross-examining a yam-killer.
Merlin is a sweet, Adorkable boy with large blue eyes and adorably large ears. He can also blast you six ways to Sunday with his awesome magical powers, especially if you threaten anyone he cares about!
In both his child and adult versions, Mordred is a slightly creepy but thoroughly adorable blue-eyed boy, and, as an adult, the "little brother" knight and a complete fanboy towards Merlin. He's also a Druid with powerful magic and ain't bad with a sword either.
Lexie "Lexipedia" Grey on Grey's Anatomy. She is one of the smartest, most promising surgical residents at Seattle Grace due in part to her photographic memory. As Derek puts it: "She has a photographic memory, we're all out of our league."
Zoe is a perky little human calculator, whose hobbies include wrestling comic book heroes come to life and making giant computers destroy themselves with the power of confusion.
Jo Grant. Cute, clumsy and pretty much The Ditz. And yet she's the only companion to have ever resisted the Master's hypnotising, as well as helping Three escape from whatever prison cell or bondage trap he'd got himself in that week.
Several incarnations of the Doctor himself are very cute at times, with it being most obvious as a stock character quirk of the Fourth Doctor (who possessed great big eyes, huge amounts of childlike wonderment and behaviour, oversized clothes even though he was enormous and a dog he would treat like a puppy). For instance, on one occasion he wanted to go around modern-day Earth Cosplaying a historically-questionable Viking and is gutted when told it is inappropriate, acting just like a little kid told to take off his costume before he can go outside. The other very cute Doctor is the Eleventh Doctor, a mixture of adorably strange and exuberant body language who likes animals and babies and chats away to them merrily, although we can only understand his side of the conversation.
When Tom Baker was asked to sum up his Doctor in one word, he said, "Adorable".
It runs in the family. Once she learns to relax on the whole "soldier" thing, the Doctor's daughter, Jenny, is all giggles and smiles as she crosses a dangerous laser field and carries her big ole gun. She also follows in her father's footsteps and, when the opportunity comes, runs for her life from a very boring planet to go and have adventures.
Clara Oswald can easily fool you into thinking she's just a short, perky, daydreaming, goofy but cute 20-something with a sharp wit and sweet, caring heart. But piss her off by threatening people in need, little kids or her friends (including the Doctor) and she'll put that wit and heart to good use and show her Badass Bookworm or Girly Bruiser side. As Weak, but Skilled, she makes up for her lack of muscle with her smarts, resourcefulness and an extremely unbreakable spirit fueled by her love for others.
Sarah Jane. This woman is adorable, kickass with a gun and will not hesitate to kill you if you put her son in danger... oh, and never threaten the Doctor if you wish to live — she has aliens who give her usually incredibly dangerous stuff to use... and a robot dog.
Spin-off Torchwood has Ianto Jones: sweet, unassuming archivist who looks younger than he is, dresses impeccably, and has a charming Welsh accent. And who will take down anyone who threatens his team, or, more specifically, his lover.
It gives us Anna Wu. While she only shows her stuff in one episode, she's such an impressive martial artist that Casey calls in a background check on her as a potential field agent. And she's certainly cute.
Chuck qualifies as Badass Adorkable. Especially with Intersect 2.0, in which he gains a plethora of new skills that causes him to say, "Uh, guys? I Know Kung-Fu!"
Detective Juliet "Jules" Ohara on Psych is blond, bubbly and is sweet to the point she gets Christmas cards from people she helped put in jail. She's also a crack shot that is not to be messed with (there's a reason that aside from Shawn she has the highest ever score on the detective exam).