Though a fairly minor character in the first season, Jory Cassel has a small, loving fanbase that remind everyone on Facebook his wonderful qualities by means of a meme called "Why We Love Jory Cassel".
Syrio Forel, the badass and Large Ham fencing master.
Hodor. Hodor? HODOR!
Greatjon Umber. In the same scene where he starts off as a bit of a jerk ass, he instantly redeems himself when he takes Robb's act of mercy upon losing two of his fingers to Grey Wind and then jokes about it and laughs it off with all the Northmen.
Jaqen H'ghar is popular for his mysterious, deadpan nature and awesome killing abilities.
Bronn the blue collar sellsword for the endless amounts of entertaining interactions between him and Tyrion and his Deadpan demeanor.
Sandor Clegane aka "the Hound," what with his terrific battle sequences and brooding personality; especially notable in relation to the books given how little screentime he comparatively has.
Barristan Selmy's got himself quite a loyal following as well considering his Memetic Badass and straight up badass traits. He even pulled off an amazing comeback scene in the Season 3 premiere when he saved Dany's life from a Manticore.
Yoren's got himself a small following as well. From looking out for Arya's safety following her father's execution and even having A Dying Moment of Awesome all to protect her and the kids he was bringing to the Night's Watch. He's also got a knife sharp enough to "shave a spider's arse".
The Spice King of Qarth's 13 gained a small following as evident by a following on Facebook that went as far to hold a memorial event page for him. It helps that not only is he a humorous and interesting character (for a character not even from the books), but for those that don't like Daenerys he provides an in-universe outlet of understandable criticism of her attitude and actions and all in the most polite and reasonable manner.
Lady Olenna Tyrell, a Cool Old Lady who got very popular, very quickly for being bitingly acerbic and frank and holding her own against many of the most powerful players in the game. Also, she kills Joffrey. That certainly didn't hurt.
Thoros of Myr is already being called the Game of Thrones version of Captain Jack Sparrow , what with his rather carefree cloud cuckoo lander attitude and outlandish approach to greeting Arya, Hot Pie, and Gendry. Also helps within a span of about five seconds he demonstrates what an amazing swordsman he is when he casts aside Arya's suspicions he's just a silly drunk and not good with a sword at all.
Margaery Tyrell's fanbase grew exponentially with each appearance of hers in Season 3. She tamed and manipulated Joffrey of all people, caused Cersei (the "Power IS Power" Queen) to start panicking, has inherited at least some of her grandma's wit and cunning, and despite her gender and age is one of the best players in the game of thrones. She is also one in-universe, having endeared herself to the smallfolk as well as much of the court (something a pure power player like Cersei deeply resents). It's also worth noting, that the expansion of her character is almost universally liked even among the book fans, good part of whom isn't usually fond of changes from the original.
Beric Dondarrion became this way before his re-appearance in Season 3 and then solidified his staus as this simply because of his presence, his status as a leader amongst a group of people fighting not for any side of the war, but for the good of the small townspeople whom are suffering the worst out of anyone in the War of the Five Kings and in the name of Robert Baratheon and Ned Stark who are both long dead and his seriously threatening reputation as a man that cannot die and even The Mountain is desperate to find and be done with. Also, his duel with Sandor was among the best duels in the series thus far.
Edmure Tully has a growing fanbase for being a hilarious Upper-Class Twit who nonetheless does his king and nephew a solid to make up for mistakes that were entirely Robb's fault.
Brynden Tully, the Blackfish, just like with the books, is one of the most popular minor characters, for being both a Cool Old Guy and for being a skullcracking badass.
Yara Greyjoy, especially after her single show-stealing scene in Season 3.
Roose Bolton — despite personally killing Robb Stark at the Red Wedding and conspiring against the whole North — actually has a growing following if the comments on Youtube and various Game of Thrones forums are to be taken into account. One cannot help respecting the man for his subterfuge, style, and the fact that he's an outright troll.
Prince Oberyn Martell was already the biggest example in the books, and he follows suit here for being thoroughly unintimidated by the Lannisters and his unusual sexual proclivities.
Pedro Pascal's passion for the role and his charisma oozing on virtually every scene he's in has ended up with people admitting that his legendarily gruesome death was actually more of a punch in the TV series than in the books.
Oberyn Martell's paramour Ellaria Sand also won over fans as one of the show's prime examples of flawless casting in Indira Varma and her abundance of exotic fan service she brings.
Locke qualifies himself in Season 4 after managing to pull off several awesome feats in combat and stealth.
Salladhor Sann, the witty and amorous pirate, gets a number of witty lines whenever chatting with Davos. Most notable is his claim that he's going to fuck Cersei as part of his price for aiding Stannis, clarifying that "he's not going to rape her, he's going to fuck her," and claiming that he's very persuasive.