It depends. If it is standing dead - how long? The best way to tell if its ready is to cut it down and visually inspect it to see if the moisture has been pulled out. Some times you can just tell from the appearance of the standing tree, but they can fool you.
With downed trees, they can be laying for quite a while, but if the ground is moist, they can still suck in water and get punky. If the bark is still on them, a tree can hold water for quite a few years until its finally bucked up and split.
Some species will dry out quicker than others.
Finally, if you're cutting standing dead timber, be very careful about falling them: dead branches can come down, and the trunks can be split, hollowed, and rotten - leaving you no holding wood after you get to a certain point.