Moss growing on trees is understandably viewed as a problem, however its presence has no direct negative effects on a tree.
It normally grows in areas that have plenty of moisture along with minimal sunlight penetration. It is also very vulnerable to air pollution, so its presence is a good indicator of clean air.
Moss can become a problem if it builds up too heavily. Excessive moss can add a significant amount of weight to branches, increasing chances of storm damage, as well as trapping moisture against the tree. This also makes the tree more vulnerable to pests and diseases.
As with many tree issues, proper pruning can help alleviate these problems.