Toaru Majutsu no Index

Toaru Majutsu no Index (Both Seasons):  C+

I give out a lot of C+s, because I feel a lot of shows are slightly better than 'just okay.'

A Certain Magical Index (to use its English title) is a mishmash of a whole lot of Anime tropes put into a blender and served with a hefty spritz of fan service (which I mostly don't mind, aside from the cloth-physics defying properties that breasts of a certain size and above seem to display).

The story takes place in Academy City, a center of research into psychic ability (which in this setting is commonplace and understood enough to justify an entire city devoted to its research).  "Ability-users" to awkwardly translate the japanese word, are classified from the powerless or extremely weak "Level 0s" to the obscenely potent Level 5s.  Our hero is a very unfortunate man named Kamijou Touma, a Level 0, who does have a power, a power that anyone with an ounce of sense would call a high level five power (don't worry, this is hardly most nonsensical thing that happens in this series, it's just the most consistently repeated): Touma's right hand has the ability to nullify and cancel any other supernatural ability it comes into contact with completely.

Touma meets the eponymous Index, a young Anglican nun when she is hanging off his balcony being 'pursued by magicians,' of which Touma is initially skeptical, but he accepts quickly when he meets a gentleman who summons a fire elemental outside his home.  Touma, being the typical protagonist, isn't particularly smart but he's always willing to risk his neck to save someone, usually one or more young women, which he will do by punching the problem with his super anti-magic/psi/divinity/whatever right hand.

The cast very quickly gets absolutely massive, but the characters are alive and interesting, if predictable.  The stories begin differently and take place in different locales with different focuses, but tend to follow a certain pattern, established early on.  The second season escalates to the point where Academy City is badly damaged, the entire Roman Catholic Church (who have a lot of mages, Magic and Religion are mostly inextricable in this series) has declared war on Science and the shadowy figures controlling the Scientific Conspiracy are beginning to come out.

I can say a lot of negative things about it (and I already have) but I should also note that I wouldn't have given it a C+ if it weren't fun.  The character designs and implementations are good, the magical system retains a solid feeling of mysticism and strangeness despite being commonplace, and the plot holds together, despite several places where you simply need to take the story's word for it, and accept that Scientists in this setting really want to be performing unethical experiments.  This is the kind of series that, if you are able to go "Okay, watching two girls who can both teleport fighting is totally awesome," you will appreciate, but if you start going, "Wait, why do Science and Magic need some sort of 'balance' in order to make the world better?  And if they need that, why does everyone seem so intent on destroying it?" the flaws in the series show up fairly readily.

There's a spinoff series, Toaru Kagaku no Railgun (A Certain Scientific Railgun) which follows one of the main protagonists and is mostly more of the same, though is less world-wrecking, a bit more personal and slightly more slice-of-life rather than Index' consistent if progressively apocalyptic plot.

Overall, if you can throw the horns and enjoy beating the tar out of over-the-top bad guys with your fists and pretty girls randomly being in various states of distress and undress, you'll love Index.  If you need a lot of internal consistency, deep emotions or any sense of restraint in your anime, Index isn't the right show for you.