1. How good do you feel you need to be in math to be a fairly competent programmer?
That depends on what you want to program. Although I think being capable of grasping the logic behind an algorithm as well as being able to think in a manner that lets you create your own is important. Increasing your mathematical knowledge can help programming skills. Some of the mathematics subjects I studied at university definitely come in handy - "Numerical Solutions to Differential Equations" is one example, while others "Einstein's Special Relativity" are fairly useless to most situations (unless of course we write a game involving objects moving close to the speed of light.)
On the other hand - I have a friend who hates mathematics, avoided studying it at school - did an Arts degree at university (ie English/Humanities/Writing) and who now writes programs for a large company that generate various scripted letters/mail. In that instance it is his writing ability more than his mathematics which is important as the actual logic is fairly simple - a lot of 'if..then' statements linked to blocks of text.
2. How do you feel about your math skills?
Happy with them, unfortunately as so much of what I learnt has little practical use in my current situation it is slowly being forgotten....