I do. Your hairstylist is providing a service. Besides a good stylist is like family. You gossip, giggle, have fun, and hopefully go home with a great style.
I've been going to the same person since I was in high school. She doesn't charge me nearly enough for the zip code. She's been cutting my kid's hair since they had it to cut! I wouldn't dream of not tipping her.
If you like the haircut it is good to tip, a lot of hair places charge rent to the hairstylist.. the tips actually help them. If you go there a lot it is not rude to wait for a specific stylist either.
If the haircut was good, then a tip is appreciated. Especially if you plan on going back to the stylist. If the haircut was horrible then do not tip, talk to the manager, they will either fix the cut or give it to you for free.