Before climbing a tree, it is imperative that you closely examine your targeted tree for dead hanging branches and other potential hazards!
It's a good idea to take a close look to see whether it will hold your weight.
Start out by walking in a circle, completely around the tree, multiple times if questionable. Start close to the trunk and move out beyond the reach of the tree's canopy. Use a pair of binoculars so that you can see the top of the tree in detail.
On the tree itself, look for broken or dead branches, cavities or cracks in the wood. You're also looking for electrical wires, poisonous plants and bees' or hornets' exiting the crown.
If decay is suspected, use a sand-filled plastic mallet to hit the trunk of the tree several times to hear if it sounds hollow. Some arborists use a long thin drip bit to measure the healthy wood residing around a hollow. Scientists believe that somewhere between 15 to 25% residual wall is considered adequate wall for self-support.
Keep in mind that as thorough as you are, inspecting trees won't make climbing them safe. Make sure you are trained, your equipment is in good shape and you are secured with strong rope any time you are in a tree.
The idea is to take the time - and the responsibility - to minimize the risk as much as possible.