Question
We've got a very tall walnut tree in the backyard and it now has black leaves on a few branches.  It doesn't seem to carry up the tree too far, mostly on the bottom branches.  We are going to have the dead branches trimmed, which might help.  Any other advice?

Answer
This sounds like aphids, the aphids are a small sofe bodied insect that sucks the juices from the plant leaves and excretes a substance called honeydew, a sooty mold will grow on the honeydew and make the leaves turn black. It is not really a large problem for older trees but the dripping will get on anything under the tree and is usually sticky. Pruning the dead limbs will not have any effect on the insects but will make the tree look better.
To control the aphids would take a sprayer that would reach all the leaves and since the leaves will be falling soon this time of the year it is not needed.

Here is a web link to more information on aphids.
http://ohioline.osu.edu/hyg-fact/2000/2031.html