Should i say happy birthday to my ex best friend?

I would just leave it. Sounds like it is a friendship that has ended and time to move on and make new friends. I don't think she would see it as being nice and being the bigger person, I would think she would see it as a way that you are trying to talk to her and get her to be your friend again. If your not talking I would defiantly keep it that way. It would be different if you guys were currently fighting and having a little tiff where you give the silent treatment for a couple days but this sounds like a permanent end to a friendship. I know its hard to do because I have been there and done that. I am glad that my ex-friend and I are no longer friends because now she is a heavy drinker and is pregnant. Just keep in mind that if she wouldn't do it she doesn't care. I hope that helped and I hope that you get things figured out soon.