Yes, definitely.
Even run of the mill business programing requires some skill at math.
Run of the mill business programing requires database skills. Being a good database programmer requires an understanding of how databases work, and what the algorithms are that the query processor uses when it translates your queries. Without an understanding of limits and derivatives (or even the basic understanding that the line y = x intersects the line y = x^2 twice), it is not feasible to accurately compare a hash-match inner join query plan vs a nested loop join query plan.
Also, a good programmer can work in just about any domain, provided that they study up a bit: games, simulation, embedded development, compilers, operating systems, web stuff, databases, etc. Being able to do all those things (or more accurately being able to quickly learn how to do all those things) requires a decent amount of mathematics background.
I'd say that one should have had some experience at some point in time with the following:
- 3 Semesters of Calc
- Diff Eq
- Linear Algebra
- Modern Algebra
- Basic probability,counting, and statistics