What is the effect of ponding water on an asphalt built-up roof?

Answer 1

Contrary to popular belief, asphalt and even rubber products do not make a roof waterproof. Both products are water resistant, but with enough time, as in standing water for long durations, these products can and will achieve saturation and allow water to pass.
I am assuming a low pitched or "flat" roof here so the two solutions that first come to mind is repitching and surfacing or tear off to deck and resurface.
There is a third option if you are assured that there are no leaks at this time and that is a waterproofed sealant like
ELMS (http://www.greenproducts.net/products/products.html)
This one has the added advantage of being a "Green Solution" and has a pretty fair track record to date. a little research on your part can find you other coatings that can achieve the end result and still fit your budget.
Good luck

Answer 2

Ponding is never good on a rooftop. Roofs are designed to drain water, you need to find out why yours isn't and fix the reason. May need to build up the area where the pond is (felt paper and more tar on top) to get the water to drain off... need to make a high spot instead of the lowspot it is...