Old topic, I know, but I'm replying anyway.
People that say "But Equestria shouldn't have racial slurs!" are completely missing the entire point of fantasy racism. When people use fantasy slurs in literature and fanfics, they often do it to underscore how short-sighed and stupid racism is without having to use real-life slurs that might offend real life people.
These are the ones I usually use, though I think I'll pick up some I see here:
Ponies in general - soft skin (by dragons)
Earth - mud pony, dirt pony
Pegasus - featherbrain, roofie (because their feathers are required for love potions)
Unicorns - horn head, telefreak
Zebras - stripe
Dragons - scale brains, scale coat, hoarder
Griffons - cat-butt, half-n-half
Breezies - gnats
Bat Pony - fang face, fruit
Alicorn - cross-breed (by unicorns, pegasai, or earths that are offended that their traits are mixed with those of lesser races)