With examples from Harry Potter and Dr. Horrible's Sing-along Blog.
The correct usage of the words reign and rein is fairly straightforward in stodgy old literal prose. It's only when things get metaphorical that the difference between them becomes a little fuzzy. The concepts they embody are awfully similar, you see, and "reign" is often at least half-sensical in contexts that call for "rein", and vice versa. And so, to the dictionary!
verb. to rule as monarch; to prevail: confusion reigned.
noun. the period of rule of a monarch; the period during which someone or something is predominant or pre-eminent.
So, to reign is to rule. Specifically, it's to rule over people, and it's something kings, passions or powerful ideas do. It's also the abstract noun that conceptualizes the authority of those who reign. For example:
The last stand at Hogwarts may have ended Voldemort's reign of terror, but anarchy would still reign in magical Britain for many months to come.
Rein, on the other hand, refers to an entirely different type of control.
verb to check or guide (a horse) by pulling on its reins; to restrain.
noun. a long, narrow strap attached at one end to a horse’s bit, used in pairs to guide or check a horse; (figurative, of reins) the power to direct and control.
Reins are steering wheels for horses, and to rein is to put the brakes on your horse. However, the term is often used figuratively, with people standing in for the horses. It is in these figurative usages that people most often mistakenly substitute "reign" for "rein", because no one likes the idea of being ridden. Here are some examples of idioms that are often saddled with "reign" when they ought to get a "rein":
Incorrect: Upon appointing Snape headmaster, Voldemort gave him free reign to run Hogwarts however he chose.
Correct: Upon appointing Snape headmaster, Voldemort gave him free rein to run Hogwarts however he chose.
Free rein refers to the authority or license to manage a situation as one sees fit. It hearkens back to a time when transportation was equine-based, and a "free rein" was held just tightly enough to feel the bit in the horse's mouth.
Take the reins:
Incorrect: Once Bad Horse announced his retirement, evidoers everywhere were immediately abuzz with rumours about who would take the reigns of the Evil League of Evil in his place.
Correct: Once Bad Horse announced his retirement, evildoers everywhere were immediately abuzz with rumours about who would take the reins of the Evil League of Evil in his place.
To take the reins means to take control of a situation or to assume authority over a group. You can't take "reigns" from anyone, because a reign is an abstract. There's only one per king, so if you were contemplating a coup, you would be trying to take away a reign, not reigns.
Incorrect: Dr. Horrible found that reigning in his anti-authoritarian tendencies to conform to the League's expectations was easier said than done.
Correct: Dr. Horrible found that reining in his anti-authoritarian tendencies to conform to the League's expectations was easier said than done.
To rein in means to restrain or moderate one's own or someone else's excessive behaviour or feelings. You can't "reign in" anything, but you can reign in a place. Spain, for instance. But that's a homonym for another day.
So whenever you're stumped over whether to use "reign" or "rein", ask yourself whether you're referring to the king, or the king's horses.
Dictionary definitions abridged from Dictionary.com