Mike:
As noted above, trees on the dam are a serious, potentially sticky issue. The rest of the trees surrounding the pond have less serious (or at least longer time-framed) affects. Leaves and other organics regularly deposited in the water effectively shorten the life of the pond by filling it in with muck, so removal is generally a good thing. You might consider leaving a few strategically located trees near the pond to serve for shade and fishing lure collection.