What you might deem an appropriate age for your parents to be paying for dinner or drinks is an entirely subjective topic informed by many factors and unique family dynamics. Is it 20 years old? Maybe 25? Or 30-something? So I’ll answer this question very personally and you can decide if you agree with me or not.
If you 1) are gainfully employed and 2) live on your own, it’s probably time to stop expecting mom and/or dad to pick up the tab. But please note that I said expecting, and not letting. Because if your parents are visiting from out of town and want to take you out to dinner, sometimes no amount of offering or even jockeying for the bill will stop them from paying. The point is that you try to pay, though, and don’t just expect them to. (If you’re a Young Person who might not be able to afford the whole bill, it’s still a nice gesture — of good manners, independence, adulthood — to offer to pay for yourself.)
For those folks who are lucky enough to have such generous parents (I count myself as one of them), do recognize your good fortune and pay it back. They probably raised you to one day go off and take care of yourself, so do them a favor and pick up the tab every now and again.