Superjail!: One could argue that the Mistress is this towards the Warden. She mainly acts tsun-tsun towards him, but every once in a while will let her dere side slip through. Combined with Belligerent Sexual Tension.
Kira Tonbo from Angelicate Avenue is completely and totally tsun-tsun to Kimi, then when spoken to by Koja, reverts to dere-dere mode.
Helga Pataki makes a prime example here. Throughout the series, she goes all dere-dere on Arnold in private and even has a shrine devoted to him, yet she can only act tsun-tsun and bully him in public. In fact, she could easily out-tsundere even the most extreme Anime tsunderes.
Rhonda could easily be seen as this for Harold, especially in "Operation Ruthless" and "An Egg Story".
It's revealed that Arnold's grandma was this when she was young.
Zuko is something of a prickly Jerk Ass most of the time, but has a soft, dorky center that he pretty much only shows around his Sugar and Ice girlfriend Mai.
Toph can come off as snarky and harsh, but she displays a much friendlier and warmer side of herself if you get to know her. Or if you're Iroh. She also likes to show affection for someone by punching their arm.
Courtney is a good example of Type A, although she can be a Type B, since she's generally polite if bossy, but if you get her mad, she gets bitchy and violent. She instantly takes a loathing for Duncan, yet she ends up falling asleep next to him in the Sucky Outdoors, and then kisses him in Basic Straining. After that, the tsundere aspect is greatly diminished after Courtney's Total Drama Actiontaking a level in jerkass. Then the tsundere act is completely dropped in World Tour. She actually becomes more of a Yandere as an example of Derailing Love Interests so the writers can pair Duncan with Gwen.
Duncan:(with his and Courtney's fake antlers stuck together) What can I say, the girl can't keep her antlers off me. (Courtney responds by kicking him in the groin)
Gwen starts out acting Tsun, takes awhile to warm up to people, but in the end she agrees to go out with Trent. By the second season they broke up. Then third season, its the same with Duncan.
Duncan is Tsun-Tsun to nearly everybody, but dere-dere to Gwen and Courtney (until the third season where he is more Tsun-Tsun to her than anybody else.)
Heather during World Tour is a perfect example of the Type A, going for the cold shoulder and insults towards Alejandro. She's even denying she likes him to Chef, and then stating in another (empty) confessional that he's "just so... perfect'!"
However, as of "African Lying Society", Heather and Alejandro are both tsundere for each other!
Murderface from Metalocalypse. Oftentimes he is rude, crude, and disrespectful to his band mates and the world around him, but occasionally becomes emotional and insecure of himself (especially in Performanceklok and Birthdayface). Creator Brendon Small describes Murderface as, "a self-hating bass player [...] thin-skinned and incredibly sensitive and just wants to be accepted constantly but can't get that because he's such a dick and pushes people away". 
Some fans believe that this is the hidden behavior of Trixie Tang toward Timmy Turner in The Fairly OddParents. In fact, in the episode Manic Mom-Day she truly behaves as a tsundere.
This was the personality given to Zelda in the animated Legend of Zelda, although usually only when dealing with Link.
Non-romantic example (most of the time): Spinelli from Recess is (usually) dere-dere towards the other five main kids, but tsun-tsun to everyone else. Also, she's the most dere-dere with T.J., whom it's hinted she has a crush on...
Ren from The Ren & Stimpy Show is one towards his best friend and life partner Stimpy. Less so in the first episodes, where apart from Ren's occasional and usually justified insults, the vitriolic part of their relationship is barely visible. But, oddly for tsunderes, his positive/neutral attitude goes downhill as episodes pass. In Adult Party Cartoon, he turns into a monster (at least, in some episodes, where it was intended as Rule of Funny, but turned out very much Dude, Not Funny!). His tsundere behaviour towards Stimpy varies between Domestic Abuse and I Shall Taunt You, with only the latter receiving any noticeable reaction. In earlier seasons, he used to have Cry Cute breakdowns fairly often, with Stimpy as his shoulder to cry on—in "Son Of Stimpy" and "The Big Shot" it's also very obviously portrayed that he cares deeply for the moronic cat, which is the "dere" side of his personality.
Vanessa Warfield from M.A.S.K. towards Brad Turner in the second season.
The Simpsons episode "Stealing First Base". Bart falls in love with Nikki, a girl in another fourth grade class. She's definitely a Type A. She goes from being upset because he stole a kiss from her, to wanting to be his girlfriend. He still can't figure her out by the end of the episode (though Bart did cry out, "I love you!" to her as she left).
Bart actually got this a couple of times. When he ends up in Juvie, he becomes the target of a tough girl who may or may not like him. Bart is as confused by this girl as he was by Nikki, though this one is more (physically) painful.
Lily from Kappa Mikey must have the diaphragm of ten lions and threatens physical pain not just on her target of affection Mikey but on the rest of the cast as well. Only once in a full moon does she admit that Mikey's sweet.
Candace of Phineas and Ferb has some aspects of this. Most noticeable in "Split Personality", in which she's split into pure Tsun Tsun and pure Dere Dere duplicates.
A rare male example: Kyle from Fanboy and Chum Chum qualifies. While usually dismissing the titular duo's pushy friendliness with snark, he has occasionally shown to crave their friendship in reality, most prominently in the episode "Sigmund the Sorcerer".
Think one male tsundere is rare? How about two of them put into the same environment? Buck Tuddrussel and Larry 3000 from Time Squad refer to each other with great amounts of disdain in their default tsun mood, but if placed in a proper situation, can be nice, open and protective over each other (though they are never at the same time). This is more prominent with Larry, who is not subject to Testosterone Poisoning.
Sarah from Ed, Edd n Eddy. It's hard to tell, because she's almost always in tsun-mode - occasionally going full-blown Ax-Crazy - but she does have her occasional dere moments, mostly toward Jimmy.
If you look at it from A Certain Point Of View, Wally aka Numbuh 4 from Codename: Kids Next Door is a male tsundere. He's the kind of kid who's crazy for action, but when Kuki's being sweet to him, he can't look at Kuki straight in the eye.
Kendall in Kick Buttowski, whenever Kicks around she acts in her tsun-mode. But when he's not looking she goes in dere-mode for him.
Rainbow Dash from My Little Pony: Friendship Is Magic can be this at times to Fluttershy, Applejack, Rarity, Pinkie Pie, and Tank, her pet tortoise. She's got a good heart, but she can be rather rude to her closest friends. She softens up in later seasons and becomes more of an Unsorted Tsundere with both Type A and Type B qualities to her. She's also a Kuudere. She even says a classic Tsundere line saying she's worried Tank will slack off and isn't worried about him. Cue Luminescent Blush.
Fluttershy's pet White Bunny Angel is also this. He is often abrasive to his mistress but he's worse to everyone else, doesn't like being separated from her yet—when she needs it—he is sweet and comforting.
Rarity's cat Opalescence showed this behavior in the presence of Rainbow Dash's tortoise Tank. The episode "Just for Sidekicks" shows her being affectionate towards him and her typical behavior towards others, but only after smacking his head once.
Rick Sanchez from Rick and Morty is a TSUNdere, being insulting and abusive but better than most alternate versions of himself.
Meg Griffin from Family Guy is a Type B. She is usually dere-dere, but acts tsun-tsun to people she doesn't like or people who usually piss her off.
Her mother Lois Griffin also applies to this. Lois is usually kind and polite with others, but she has an aggressive and short-tempered side, usually caused by her husband Peter's stupidity, impulsiveness, and eccentric plans that often blow up in his face.
X-Men: Evolution: Miss Jean Grey normally acts like a sweet and cheerful Cool Big Sis towards the younger kids, but goes cranky when Scott or Duncan are around, though mostly when they're being idiots or butting heads. Then there's her hidden jealousy against Rogue or Taryn...
Then there's Annabelle, the angelic whippet from All Dogs Go to Heaven. "Touch that watch and you can never go back...I SAID TOUCH THAT WATCH AND YOU CAN NEVER GO BACK!"
Astrid from the film How to Train Your Dragon. She initially disliked Hiccup (the main character) and was violent towards him, but after discovering his peace-making with dragons and his bond with Toothless, her attitude softens considerably and she develops a romantic interest in him. She still continues her hitting with Hiccup, but becomes more "dere" than "tsun", particularly in the sequel.
(after putting himself in danger)
Astrid: (suddenly punches Hiccup) That's for scaring me.
Hiccup: (annoyed) W-What?! W-ha ... is it always gonna be this way?! Cause ...
(Astrid suddenly kisses him)
Hiccup: ... I could get used to it.
Mitsuki from Kappa Mikey, for Mikey. She is soft, dependent, shy, and kind the point where nobody else acknowledges her and they often forget her name, but in one episode it's revealed that she used to be a secret agent before breaking into show business and can injure nearly anyone if need be.
Frankie from Foster's Home for Imaginary Friends is very warm and nurturing towards the imaginary friends, but doesn't take too kindly to Mr. Herriman's pestering or Bloo's madness.
Maurecia from Wayside is a Genki Girl who is extremely friendly and liked by everyone in Wayside School. And she expresses her unrequited love for Todd by hitting him, constantly.
June from KaBlam! is usually sweet and laid-back. However, when something bad happens (like Henry giving her crap or something won't go her way), she's pretty tough. She's also always doing something mean to Henry (even though they're friends), however, she has a huge crush on him.
By contrast to the obvious Type A William Murderface, Toki Wartooth from Metalocalypse is a Type B tsundere, usually being the nicest guy in the band, and treats every band member with a calm attitude... Except Skwisgaar, to whom he is specifically tsun towards. Still, it is pretty obvious that he does have a crush on him. Yes, a male tsundere having the hots for another male character.
Princess Luna too, as seen in her Season 2 debut. Her emotions and personality paint her as such when only the audience (and then Twilight) get to see how hurt she really feels.
Turanga Leela from Futurama. She has a love for violence and hit mostly everyone at least once, besides her love interest Fry. She is usually a Type B but Fry makes her irritated often, especially in the beginning. His stupidness, annoyingness, and immaturity brings it out of her turning her into a Type A. Leela at first didn't feel the same but as the series progressed, she fell in love with him, in part to Fry's persistence and also his consideration of her feelings.
Leela: "Fry, you idiot! You noble idiot!"
Tasha in The Backyardigans might be one of those. Most of the time, she's bossy and wants everything her way, but during the "Giant Problem" episode she becomes a playful Genki Girl Giant.
Gwen Tennyson in Ben 10. She was Type A as a kid, she becomes a Type B, but towards Kevin and Ben.
Probably the only noteworthy thing about the most recent Fantastic Four animated series was that Sue went from being an extreme dere (a dere-mat, actually) to almost a Type A — although with those three guys, it's understandable. This was probably spun off from her updated profile in the comics — she's much more aggressive with her powers, to the point where she's now regarded as the most powerful member of the team.
Velma in Scooby-Doo! Mystery Incorporated has become this, being sweet and romantic when she's alone with Shaggy but then becoming aloof and irritated when Scooby horns in.
Minerva Mink from Animaniacs. For the most part, she's Tsun-Tsun, but at the end of any of her skits, she'll go Dere-Dere towards an attractive male.
Kimmy in Sym-Bionic Titan seems to go back and forth between both types. She's introduced to us as being rather cold and snobby, but she becomes sweeter as she warms up to Newton.