I'm a former high school/collegiate hurdler, so I'll toss in my 2 cents....
I think flexibility (particularly in the lower body) is key. One of the most important things about getting over hurdles quickly is trying to avoid being airborn too long. And that means you need to stay low and create very little space between you and the hurldle as you pass over. If you're inflexible this is very difficult to do efficiently and you tend to crash into the hurdles more. Crashing into the hurdles not only slows you down but it can throw off your rythmn and steps, which is a recipe for disaster in the 110s.
Women are usually better hurdlers than men, which has something to do with the fact that they are usually a bit more flexible. Notice the way they just graze over those hurdles without touching them. Women just lack the raw speed to run with the men. If you gave Gail Devers (in her prime) the raw speed of say - Terrance Trammell, she would have destroyed the likes of Trammell, Johnson, Xiang, etc in the 110 hurdles. Of course, height is also a factor, but my point is - flexibility makes you a better hurdler.
It's less important in the 300/400m hurdles.
Obviously to be a competitive hurdler at a high level you're also going to need excellent speed. Trammell was the Indoor 60m Champ a few years back. I'm no Trammell, but I was my school's record holder in the 55m and 200m (state qualifier in both), so I had speed. It also helps if you aren't a midget. But against other hurdlers who have similar speed and height, you will be at the advantage if you are flexible.