My Arab is the only one I've ever ridden significantly (2 years) and recently enough to remember (haha) and she's only done "the head flip" once. We were galloping, she wanted to run away with me, I got mad at her, and she realized that it would be in her best interest to slow down, then she engaged in the head flip in a very "I don't wanna but I will" way. Haha
I've heard that it can be common for Arabs to flip their heads around (if you mean the horses flipped their heads around, not throwing them in the air) but it's the same with the idiosyncrasies of every breed: some will do it, some won't.
If you mean that these Arabs you rode kept throwing their heads in the air, then I would definitely look into saddle fit and how you're riding. =)
Fabio - 13 year old Arab/QH gelding
Hazel - 14 year old Angora goat
Atticus - 4 year old LaMancha/Alpine cross goat
Rest peacefully, Lacey.