Any woven fabric will fray at least a little. Lighter fabrics with a loose weave (ex: chiffon, the crappy brocade from Joann's) typically fray more than those with a tighter weave (ex: canvas, twill) tends to fray less. Fiber content also has some effect. Natural fibers tend to ravel less (my own experience leads me to believe that wool is the least ravely, followed by linen, cotton, and then silk) than synthetics like polyester when all other factors are equal.
Sometimes, to make the really ravely ones less of a headache, I go ahead and cut it with pinking shears--dramatically reduces fraying.
Fluttershy (MLP), Lady Loki (Thor comics)
Joffery Baratheon (Game of Thrones)
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