I've mostly stopped. There's few enough people doing it in my town that I'm starting to know some of them and frankly I hate liars. This one guy finally pissed me off to the point where I've mostly stopped because every time he'd basically tie me up with this sad story for 5 minutes and it was always the same story. Fan belt broke in his car on the interstate, guy wants 300 bucks to fix it(lol), just trying to get home and his wife and baby are stuck in the car. After hearing the same old story God knows how many times over the months(maybe years) by the same guy I finally called him out on it and of course that apparently was a racist thing for me to do and I got pissed and since then I've just stopped carrying money altogether. If someone comes up to me and asks for food, gas or a ride I don't mind but I've stopped dealing with money.
And the thing is, I wouldn't even be mad if the guy was just honest to me, but when begging is, I guess your job, and you're in a small enough town and your area is a small area that you work, don't be surprised if people get to know you.