The first and primary protagonist. He appears in basically all the works at some point or another. Academy city considers him a Level 0. He attends a Certain Highschool (name unknown).
He has the ability ｢幻想殺し(イマジンブレイカー)｣ - ｢Imagine Breaker｣ which resides in his right hand. It lets him cancel out all supernatural phenomena, whether it originates in science or magic. One less than ideal side-effect of this is his misfortune. Because he cancels out all supernatural phenomena, he also cancels out divine blessings and luck. This leads to his de-facto catchphrase: ‘Such misfortune!’
He’s a person with a kind heart. When someone asks him for help, he will help them no-questions-asked… sometimes he helps even when they don’t ask.
Touma has a sort-of internal sense of right and wrong, not governed by societal norms.
In day-to-day life, he worries about not having enough cash to buy himself food. He’s a bit book-dumb, exemplified by his need to attend make-up classes for his make-up classes for his make-up classes for having a failing grade in school.
At the end of the first Volume (first arc in the anime) he loses his memory and starts pretending he hasn’t. This lasts until the last Volume of the first Index series. This is actually one of my favorite aspects of his character, only because he pretends he knows what’s going on 90% of the time… to not reveal he lost his memory.
He lives with Index and her cat Sphynx (or, more accurately, they live with him). People say it doesn’t make sense because of how annoying she is. They seem to miss that Touma actually likes Index.

Temporary addition: One implication that is there but nobody seems to have noticed is that Kamijou’s arm cancels out all supernatural abilities, including any he may have himself. This means that Kamijou, having gone through the Esper Development Program, may actually have Esper abilities beyond Level 0 but, if he does, they never manifest due to the damn arm. I vaguely remember that the phrasing in one of the Light Novels directly implied this to be the case.
Now…that might mean that Kamijou’s real Esper ability will only manifest whenever his arm is chopped off. But since he doesn’t know what this potential Esper ability is, he probably never activates it (assuming he isn’t Level 0).