I would say you definitely don't need to be good at math to be a good programmer.

My first job as a programmer was doing 3D graphics for B-52 and Cruise Missile mission planning. It was a math intensive application, but I really only needed access to people that were good/great in math. I didn't need to know the formula for computing great circle distances between two points. I did need to know how to convert the formula so that it worked in a programming language. The same with flight simulation. Boeing did all the math we just had to apply it.

That experience also helped me get a sense of who would be a good programmer and who wouldn't. The job had pilots and navigators taking a tour of duty as programmers and to help the programmers understand the needs of the mission. You could usually tell within a few weeks what pilots and navigators would be good at it. Math majors usually took to programming right away.

So I would say being good at math makes it more likely you will be good at programming, but I know a lot of good programmers that aren't so good at math.