Koyomi Araragi is a third year high school student who survived a vampire attack during spring break and barely regained his human life in the time that followed as a boy with remnants of vampiric traits. He can see in the dark, his eyes turn red when he gets angry, and he heals incredibly fast. As a result, he questions his lifespan. He remains scared of morning sunlight despite the fact that it no longer has any negative effects on him.
Koyomi is a laid-back person whose only real friend at school is Tsubasa Hanekawa. He's a poor student, close to failing every class except math.
It is revealed through conversations that he's quite knowledgeable with anime; a fact even noted by Nadeko Sengoku once.
Although he is shown to be attracted to the other girls, he turns their advances down due to his loyalty to Hitagi.
Other characters seems to speculate that Koyomi is a lolicon, particularly Mayoi and Hitagi, with Hitagi thinking that Nadeko is a "threat" to her.
He is very noble, which is why Hitagi is attracted to him. He is willing to help others at the cost of his own life. As such, the female characters he has helped are quite attached to him. He feels most comfortable talking to Mayoi, Shinobu and, from the Second Season on, to Yotsugi about his problems.
Koyomi is the only person who thinks that his family relationship is bad, with Karen and Tsukihi thinking otherwise. His parents were revealed to be police officers.
His personality is portrayed more clearly in the novels, where his inner thoughts show him to be much more perverted and intelligent than the anime leads one to believe.
Due to events prior to Kizumonogatari and Bakemonogatari, Koyomi avoided having friends and seemed to have lost faith and trust in people and himself.