Question
I live in Maryland. I have a maple tree in my yard that is more than 60 years old. The tree has several large branches with holes. I notice birds and squirrels seem to be moving in and out of these holes. These large limbs bloom every year and seem to appear healthy. My question, do the holes indicate the tree is not healthy? Is the tree in danger?

Answer
Sounds like a decay fungi has entered the tree through a wound and has caused the tree to start to become hollow.

Here is some information on a hollow tree.
The heartwood consists of the growth rings in the center of the trunk. They are aged sapwood and thus form part of the Xylem. They tend to have a darker color than the sapwood, because they no longer transport any water and are therefore much drier, and they tend to be clogged up with gums, resins and other substances, depending on tree species. Because they are no longer taking part in the trees vital processes, they can be said to be 'dead wood'.
A hollow tree is a tree where the heartwood, which has less resistance to rot than the living parts, has gradually decayed away. Surprisingly, this makes no difference to the vigor of the tree and may even enhance it ability to stand up to severe gales, due to the immense strength of a tubular structure. So it is important to realize that a tree with decaying heartwood is NOT a decaying tree! It is a natural process in many older trees and makes them all the more valuable as a habitat for many different forms of wildlife.  
The living part of a tree is the layer of cells just under the bark called the cambium layer. The decay fungi do not infect the cambium cells but only decay dead wood calls -the inner part of a tree. Over time the tree will lay down guard cells to keep the decay from spreading . Compartmentalization is a word that is used when talking about hollow trees and these cells.

The only danger would be if the hollow gets too large the tree could break but this is a low chance and nothing to really worry about.
I would recommend that you fertilize the tree with 10-10-10 fertilizer at the rate of 1 lb per inch of trunk diameter scattered around the tree and watered in good. Apply the fertilizer just before a rain storm and you will not need to water. This will increase the overall health of the tree.