It’s a story as old as time itself; boy lives in a science-based city filled with espers of various power levels, boy meets girl, girl turns out to be the living repository of every forbidden magical spell the Church has banned. Hijinks ensue.
The boy is Touma Kamijou, and his esper level is zero, the lowest; his right hand is called the Imagine Breaker, and can counteract any magical or esper power it touches. The main side effect is that it has made him the unluckiest person alive.
The girl is known only as Index, and she’s escaped from her handlers at the Church of England and run into Touma at his apartment in Academy City.
Together, they fight crime!
Touma tries to defend Index from the Church minions sent to reclaim her, and in the process learns of the existence of magic. Index is amazed by science. Through the 24 episode run, in addition to a few monster-of-the-week stories, there are several longer multi-episode plot lines that follow the plots of the light novels. The best of these is known as the Little Sisters arc, where Touma faces off against a level 5 esper known as Accelerator, and tries to stop him from killing enough level 3 clones of another esper to grind his way to level 6.
It’s dark at times, and funny at times, but nearly the whole run is solidly written (if you can stand the explanations they give you every so often, anyway).
Funimation licenced A Certain Magical Index for release this year, but it’s not out yet.