I have been through several levels of Calculus, and, admittedly, have never actually used Calculus in any of my programming jobs; but I didn't get high enough into the theory of things to need it. I did some work with biometric scanners, but not the theory end. I just missed a job programming laser cutters that sounded like it would use fairly decent math. I've had one boss and one teacher who worked at NASA; and I wouldn't expect anything that cool without some serious math.
OTOH, I am pretty good at basic math through trig (partly from the calc classes), and it has been a huge help to me in most of my dev jobs. I've had a few positions alongside non-mathy programmers, and I ran circles around them. I once took a professional developer's code, and reduced dozens of complex lines down to three simple math equations. There was nothing exactly *wrong* with his code (except he was getting a logic bug he couldn't find), but three lines is way easier to maintain, and it's a lot more fun to write.
If you want to do anything with networking, masks are easier to do if you understand boolean logic well. If you want to write games--especially graphics--you can be a lot more efficient if you're good at math (and more efficient=faster). Text manipulation is easier to do when you get things such as capitalizing a letter just means subtracting 32 from it. Twiddling the calendar is easier when you get that a month is 30.6 days, and how that reduces date math to a division and an addition.
So, no; you don't need math--all of that is doable without, as long as you have the libraries, etc--any more than you need to be a good runner to enter a marathon. But being good at math will make you more competitive, and a better programmer, and will give you better tools for problem-solving.
Hiring-wise, I would take a candidate that is good at math over a more experienced one who isn't.
"Trust me. I know what I'm doing." -- Sledge Hammer