i don't have trees in the best places to use regularly in my back yard, but i've herd of others talk about using the same trees in their yard on a fairly regular basis w/ no sign of stress on the trees.
this is an area that could use a lot more research (collecting precise & useful data), but my basic thoughts at this time are that just like staying warm, there are a number of variables...
type of tree
size of tree
age of tree
condition of tree
type of hammock support
method of attaching hammock support to tree
amount of sag
weight of the loaded hammock
how much swinging the hammocker does
there are more no doubt but that's a start<G>.