Asakura Twins (Shaman King) - Hao is the 'bad guy' whereas Yoh is the opposite. In anime Yoh hold an hate towards his brother as he wanted to become the shaman king while treating other people like rubbish. In manga they seem getting along better. They are called as parts of one soul therefore Hao wanted to devour Yoh in the end of anime.
Hiiragi Twins (Lucky Star) - Their characters are opposite; Tsukasa is very good at cooking and very friendly yet her weak point is school work whereas Kagami is a smart student where everybody seeks help however she's sometimes egoistical and is bad at cooking and household chores
Orihara Twins (Durarara!!) - Unfortunately these two girls had only a tribut in one episode. They have a very close relationship togather and have the same obssession to an actor - Yuuhei Heiwajima. Her close relationship may be a result of Izaya pushing them away. They are never saw being apart from each other
Misaki Twins (Another) - They look identical, also they do that in purpose; like dress similary. They were seperated so they were meeting in secret and become best friends. They share a lot with each other and both have interest in dolls. Mei and Fujioka were very attached to each other.
Sonozaki Twins (Higurashi no naku koro ni) - As the whole plot is confusing Mion and Shion are getting well overall. They switched places when attending the family meetings and even though they haven't see each other for long period of time they open their heart to each other. In the 'torture' moment of the anime Shion wasn't afraid of her sister overall which may seem like the have bad relationship. Shion was just afraid of Mion's behaviour as she may hurt Keichii.....
Fujibayashi Twins (Clannad) - Kyou is the tsundere type girl with long hair who is always protective towards her sister. Ryou whereas is calm and caring. They are two totally different girls who get on well as siblings.
Rozen Doll Twins (Rozen Maiden) - They aren't really twins. Barasuishou (purple) was made by Rozen's student, who based her by the real 7th doll. They both hold an insane personality though and their aims are a bit similar too. Kirakishou only appears in manga whereas Barasuishou only in anime.
Italy Twins (Hetalia) - They both have different personality as Italy is calm, friendly and very cheerful whereas Romano is tough, bad-tempered and sometimes aggresive yet he has the cute shy side like his brother. Yet, they both are extreme cowards. They don't get along well as Romano is the person that bullies his brother and doesn't accept his existence.
Kiryuu Twins (Vampire Knight) - Ichiru and Zero were cursed twins which belong to Vampire Hunting family. They should be one person and Zero as the oldest twin should have devoured his brother in the womb. Ichiru was very jelous and in despair which caused trouble to the whole family. Zero even though he hates his twin, inside there's a bit of love left in his heart. They had a close relationship when young however Ichiru started to hate his brother.
Hitachiin Twins (Ouran Highschool Host club) - They always had a close relationship. Before attending Ouran club they were socially awkward and only considered themselves, yet after they decided to open up to people. It's nearly impossible to tell who is which. They both are very lively and humorous therefore they have good time togather.
Asahina Triplets (Brothers Conflict) - Well not twins but triplets who aren't really so identical except few traits. Azusa and Tsubaki are more alike not only with interest but also with appearance. They hold closer relationship as they work in the same industry, but they still keep contact withe their brother. All three have a spot on their face and purple eyes.
Alyss and Alice (Pandora Hearts) - They were both born in the abyss however Alice was placed afterwards in the real world. They are able to exchange their souls. She used to be 'one' with the Will of the Abyss yet then she separated as another part to join Oz in the real world.
Post Question: Are they any other anime twins which weren't mentioned above?
Which is your favourite anime twin?