What is the difference between "horrify" and "terrify"?

To add to Will's answer, I think there is an element of shock and surprise in 'horrify' which there isn't in 'terrify'.

I could quite easily continue to be terrified by something that terrified me yesterday, whereas I think that if I was horrified by something yesterday, today I'm more likely just disgusted.

As an interesting aside, note that horrify:horrific <> terrify:terrific.

Even though Mary Shelley's monster terrorized both its creator, Dr Frankenstein, and the surrounding village, it is in the genre of Gothic horror. I think this is because the reader is horrified at Dr. Frankenstein's obsession with working with dead bodies and creating life from death.

This work makes you feel horror (revulsion) rather than terror (fear).

Horror is something that, on an elemental level, makes you feel absolute revulsion and rejection. I am horrified when I read about mothers who murdered their infants by microwaving them. My gut just clenches and turns on itself with the thought of what that child went through before it died.

Terror is something that invokes an instinctual 'fight or flight' response - someone sneaking up behind you and scaring you, the sensation of centipedes running over your skin - it makes your heart race and your adrenaline rush.

My professor of Shakespeare taught that terror makes you flee (people will run away from a terrorist bombing) while horror draws you in (people are transfixed by horror movies and deadly car wrecks). Terror = run; horror = stop and stare.

For me, terror is something similar to a gnawing, escalating sensation of something really awful afoot or likely to happen. The word "dread" comes to mind and having just checked the Wikipedia article mentioned earlier in this thread, I now see that at least one reference supports this notion I have for this word. Horror, on the other hand, is something more sudden and intense. Perhaps an example from film can better illustrate what these words mean to me.

[SPOILER ALERT! STOP READING IF YOU'VE NEVER SEEN ROSEMARY'S BABY]

The film Rosemary's Baby comes to mind most prominently when I think of a movie that illustrates well the difference between terror and horror. When Rosemary starts putting various odd clues together and comes to suspect that she has, unknowingly, become part of a sinister plot at the hands of a Satanic cult, she becomes more and more terrified. This terror grows and grows and grows until she becomes hysterical and then goes into labor and gives birth. I'll fast forward through some details, but eventually, she comes face to face with her baby and is horrified by the sight of it.