This is a very hard question to answer and will likely stir up a lot of debate.

One of the reasons why this question is so hard is that it partly depends upon what type of work you are doing. There is not a lot of math involved with most business applications, so you can get by with a solid understanding of algebra and business math. However, more advanced applications call for more advanced math and you start needing a solid understanding of calculus, linear algebra, and the like.

However, that is just one part of the equation in that you still need a certain degree of mathematics for just the practice of programming itself. It goes without saying that you need to be comfortable with logic to just be able to write a basic program as well as basic algebra. Looking a bit beyond just getting a basic program working though you need to have an understanding of certain aspects of discrete mathematics to be able to make determination as to what makes for a good algorithm to use for a given problem.

To get back to the heart of the question though. I personally don't think you need to be a mathematician to be a good programmer; however, I do think that you need to be comfortable with math to be able to be a good generalist programmer.