My ex boyfriend dumped me 4 months ago, out of the blue. It was hard, but I've moved on. We haven't really kept in contact as friends. Should I wish him a happy birthday out of courtesy? I haven't harbored any grudges per se. Part of me thinks that I was too amicable during the breakup, as he didn't exactly show me the honesty and respect that our 2 and a half year relationship deserved. I don't want to be rude, but I don't want awkward situations either, when we run into each other.

No. You've moved on. Keep moving.

He does not deserve a birthday greeting fom you. Glad to see that you are moving on. Never second guess yourself on how you handle a situation. You did what came naturally to you and you are a better person for it. If you see him in public and wish to speak to him, that's up to you. He deserves nothing from you, that you do not want to give.