The other day I saw a couple hail a cab and at first the cabbie shook his head after hearing their destination and started to pull away.
I gave thought to catching the cab's number and reporting him. I don't know if he saw my stare (though he did see me, we made semi eye contact), but he stopped and called to the couple and told them he'd take them where they want to go.
I've posted this before, but it's worth repeating:
If you are in any of the boroughs, and you hail a cab that is on duty (you'd know that from the light sequence) they cannot refuse you. Also, all cabs must be capable of taking credit cards. If their machine isn't working, it's their responsibility to let you know, so if you don't have cash you can get a different cab. Keep in mind, however, that when you pay with a card, the drivers lose a certain amount of the fare to the card company. In other words, unless you had a near death experience, you should give a good tip to make up for paying with a card.