The term "Miracle Rookie" refers to a character who suddenly becomes an instant expert at anything despite having no training or any experience in the task they are doing, a lot of them are annoying Mary Sue types who usually have the added bonus of being the show's main problem solver. So on to the list, I have a few choice words about these characters as well.
Dishonorable Mentions
Yui Hirasawa from K-On
Most of her so called Guitar work maybe from Autism as Yui demonstrates symptoms of Hyper Focus where she can focus and master anything at the cost of forgetting something else. Autism is not an excuse to go on this list.
Kazuya Aoi from Freezing
Can somehow control Satellizer after meeting her once, justified as he's the brother of a stronger character.
Ichika Orimura from Infinite Stratos
The same can be said for Ichika who also has a more famous sister who is a master of her craft.
10. Ash Ketchum from Pokemon
Rated low as he never wins the Pokemon League but it doesn't excuse the fact that he seems to make friends with everyone he meets and somehow wins respect of all legendary Pokemon. For a normal trainer that doesn't happen.
9. Negi Springfield from Negima
Doesn't seem limited by the fact that he's only ten, in fact he spends so much time acting out of age that you don't see the same character you started with and he seemingly achieves all this without any effort.
8. Uzumaki Naruto from Naruto
From Mastering clone jutsu after reading one scroll to being Ninja Jesus, Naruto seems to do an Ash and befriend everyone he meets and seems to be stronger than even the strongest characters in the anime.
7. Minato Sahashi from Sekirei
Gets dragged into the whole Sekirei story by accident and suddenly commands a harem of super powered girls. Then starts being all high and mighty about saving all the Sekirei.
6. Saito Hiraga from Familiar of Zero
Gets sucked into a new world and suddenly masters everything from swords to piloting World War II fighter jets and turns the nobility cycle upside down in the process, the only reason he's not higher is because I actually feel sorry for him having to spend his days with Louise.
5. Madoka Kaname from Madoka Magica
Much of the story is about preventing her from becoming a Magical Girl but no matter how you look at it, she's still insufferable as a character and her final form makes Naruto's achievements look like nothing.
4. Akane Isshiki from Vividred Operation
I do like this series but I find Akane annoying, she seems to command everything with ease and makes friends instantly without even trying, if the series were a bit longer and had some development it would be excused but the rush in getting to the climax makes Akane too perfect as a character and it's irritating.
3. Misaki Suzuhara from Angelic Layer
She invented the term Miracle Rookie, Misaki somehow gets dragged into the Angelic Layer game but somehow manages to win nearly all her battles by a mixture of luck or convenient wrestling moves she saw her friend perform. It doesn't help that her angel Hikaru can take a huge pounding and still stand and counter with something stronger that finishes off her opponent in one hit. The balance of powers in this anime is like a fighting character with a million cheat codes.
2. Kamille Bidan from Zeta Gundam
All he had to do was shrug off an insult from a Titans Pilot and we could've avoided the whole Zeta Gundam series. While most Gundam pilots starting out, find themselves in this position, Kamille is the worst offender of this. Unlike the other people on this list who are kind and pariahs of benevolence, Kamille is a complete utter ass hole who thinks he has the god given right to preach to everyone, no wonder people punch him so much.
1. Yoshika Miyafuji from Strike Witches
But this girl almost made Strike Witches unwatchable. Yoshika seems to defy logic in this series, how is it that a young girl whose only talent is healing and creating barriers somehow seems to do better than veteran witches in this war going to the point of solving every problem and effectively leading the 501st Strike Witches despite not being an actual leader and then seemingly smiles all the time thinking everything is okay and cheery when countries are being destroyed by rogue aliens. Seriously it's irritating.