Ren Mihashi is lacking in confidence and even often stammers and trails off when talking (as a result of severe bullying).  He completely smashes the mold as those qualities are typically not seen in pitchers for baseball anime.

Light Yagami has a god-complex and sees himself as the bringer of justice when the world sees him as the bad guy.  He avoids detection for so long because of his wits.

Shinichi Kudo/Conan Edogawa, while retaining some 'typical' qualities (disregard for his safety, willingness to jump into a situation) isn't just described as 'Holmes of the Heisei era' for no reason.  Contemplative, typically level headed, and highly intelligent and adaptive are traits which puts this anime on the list.

It might be odd to see a Digimon anime on this list, but Takato Matsuda has a mixed bag of protagonist traits.  While boasting kindness and an eagerness to do the right thing, there are many times he was legit afraid...including of his very first encounter with his partner, Guilmon.  He's not very confident, and is very unsure in a leadership position.  He isn't as "let's do this" as previous Digimon protagonists were, so I have to include Tamers on the list.

Edward Elric is clever, crafty, snarky, and above all:  extremely intelligent.  While he does still carry many traits of the typical protagonist (a big heart/caring for others, a disregard for his own safety, and a fiery personality), he's just enough to put him on this list.

The one claiming the name of William James Moriarty is a genius; cold and calculating, and the lord of the underground.  He will set up crimes on the greedy elite in ways which has Scotland Yard, and the typical person, completely baffled.

Kenshin Himura breaks the mold by being an older protagonist in a shounen anime; clocking in at 27 years old.  Due to maturity and his past, he is smart and looks before he leaps. 

While arguably all four main characters have somewhat of an equal bid for the 'protagonist', Genjo Sanzo is definitely its main character...and he's the opposite of the typical protagonist:  He's chill, sometimes cold, callus, has bad habits, and isn't easily surprised. 

Hakkai also works against the typical protagonist, so having two out of four characters breaking the mold puts this anime on the list.

Yoh Asakura is lazy, unmotivated, and has a very 'que sera sera' (or in his words, 'nanto ko naru') approach to life.

Lina Inverse does have a fiery temper, but she isn't the typical selfless character.  She tends to make sure she has a reward lined up if she's to do something, and intelligent.

Shinpei Ajiro has an ability to take a step back and sort of remove himself from the situation (similar to dissociating) to remain cool and calm even in an emotional situation.  He's not the typical knee-jerk reactive protagonist, and a later point in the plot sees him trying to outsmart an almost omnipotent enemy in a Final Problem (Holmes vs Moriarty showdown) sort of fashion.

Heine Wittgenstein is a no-nonsense character with a very deadpan way of going through things...though being a mature adult certainly helps put him on this list.  He looks before he leaps, but will leap with a quiet confidence instead of a boastful one like most protagonists tend to do.

As I say in my review, Iruma is a complete doormat.  He certainly does have a lot of typical protagonist vibes, but he's also hesitant to jump into the fray of battle and isn't very confident in himself at first.  He's perfectly fine with accepting help from his friends rather than trying to do everything himself for glory...in fact, Iruma would rather stay out of the spotlight.

Yugi Mutou is shy and lacks confidence.  He's talented, but is complete bully bait, and is actually rather weak (as his other half has to take over when things get dicey).

Yugi Mutou is shy and lacks confidence.  There are times (typically towards the start) when he feels the pressure and nearly gives up, and needs help to keep his head held high.