So you need an anime which actively tries to look like a stereotype (since you want the stereotype breakdown to be intentional? If the anime premise isn't steoreotypical you would hardly expect stereotypical characters) with stereotype characters, but where the characters unfolds in a way you didn't expect. Which is harder the more you watch since there is barely fundamntally original. Your "something girly, highly emotional boy or a boyish, protective or easy going girl" sounds like cliché characters on the other extreme, parodies.
Probably intentional steoreotype break-down:
Arete Hime - seems like an ordinary tale and characters when you start watching, but I assure you it is not.
Princess Tutu - seemingly normal mahou shoujo with classical music and ballet, but both story and characters are pretty original.
Koi Kaze - Incest love story with characters that actually fall in love and ARE blood-related.
More on the parodyside:
Brigadoon - Saying this is a parody is really oversimplifying it, it definitely has an original story and touch to stand on its own. A potpurri of many genres and elements such as shoujo, mecha and much more. On the wacky side even though it has cute girls. Most people won't like it, and if you generally don't like Gainax-style you should avoid it.
Oh! Edo Rocket - Creators get a pretty free leash and this is what happens. Like Brigadoon it covers many element, like Japanese history, and has enough to stand on its own. The villains are true gems. Also on the wacky side and not always sensible, so avoid if you can't stand that.
Excel Saga - Well, you just can't leave out Excel Saga from this genre, although it's stereotypical breakdown to the other extreme that they still are steoreotypes.
Dai Mahou Touge - Parody on the mahou shoujo genre with extreme violence and gore.
Golden Boy - As someone else here recently put it, Kintarou actually gives a reason for ecchi girls to like him, rather than them to swarm around a loser for no reason. And he runs from them!
Probably not so intentional steoreotype break-down but rather a case with well done characters:
Sekai no Monshou - Strong, intelligent girl who isn't tsundere, which is a really uncommon trait. Boy who is just solid and sympathetic without any high or low points at all, and void of any irony on top of it, which is even more rare.
Honey and Clover - Does not actively try to breakdown actual steoreotypes, but characters are so fleshed out as the series progresses (Morita's weird behaviour and personality is explained for example). You can understand and feel with each of them.
NHK ni Youkoso! - Probably also not intentional steoreotype breakdown, but the extent the characters' obsession and paronoia reaches make it original and entertaining.
Baccano! - Actually the characters are remarkable steoreotypes but the impression is not.
Victorian Romance Emma - Love that cannot be, but unusually realistic characters in this type of story. Otherwise they tend to be overly into eachother, or tsundere.
Ookiku Furikabutte - As far from a main character in sports show you will get. A girlish boy with no confidence at all but still wants to be the pitcher at the costs of others.
Lovely Complex - Unusually good and versitile characters for being a shoujo. Loud girl that isn't tsundere.
Hanada Shounen-shi - Very loud boy who doesn't have a heart but still has.
Nodame Cantabile - Another show that might not do it intentionally, but still does because the characters are properly directed.
Kurenai - This show basically lives on its characters, although it isn't gound-breaking.
Zettai Shounen - Solid characters in a really slow mystery show.
Yomigaeru Sora -Rescue Wings- - Realistic characters with bits that aren't touched upon much by anime in general.
Master Keaton - Versitile realistic characters.
Monster - Versitile realistic characters.
Gungrave - I remember the characters being more than you could catch and guess at first glance.
Gankutsuou - The whole experience is quite unique.
Kareshi Kanojo no Jijou - Granted it seems pretty cliché nowadays, but I still can't think of many equivalent characters that are worth to be mentioned in the same breath.
Suzumiya Haruhi no Yuuutsu - Haruhi and Kyon were pretty original when they came, although the praised character of Kyon is practically on the verge to be a stereotype nowadays.
