Question
I have several trees in my yard that drop brnaches from time to time depending on the weather, i.e. wind and storms. Every now and then when I pick these branches up, I find some of them with a jelly-like substance on them. What is this stuff? My 'forest' consists of oaks, maples, poplars, birches and the occasional pine. I've found this substance on all of the different types of trees.

Answer
These are types of fungi called decay fungi. The infect dead wood as part of the process of nature to break down the wood. On dead branches they break down the wood cells aiding in the tree shedding the dead branches and when the branch is on the ground the actions of the fungi continue to break down the woody cells causing the branch to rot. These fungi do not attack living cells so will not effect the health of the living trees. They infect after the branch has died. The jelly is the fruiting body of the fungi. The fungi lives in the wood and to reproduce they will send out these fruiting bodies (flowers). Spores will be produced on the jelly and the spores will be blown to other woody cells.
Some of these jelly looking growths may also be lichens. A lichen is not a single organism the way most other living things are, but rather it is a combination of two organisms which live together intimately. Most of the lichen is composed of fungal filaments, but living among the filaments are algal cells. During moist weather the lichens will also produce fruiting bodies. They live on the outer bark of a tree for the most part.  These also do not harm the living tree.
More than likely it is the decay fungi but there should be no worry about them harming your living trees.