What is the easiest way to shred chicken?
Once it's cooled down some, I switch to using my hands ... expecially as it helps to find any bones, globs of fat, etc.  I find it goes much faster, particularly if you're dealing with anything other than boneless breast meat.

... but it shreds easiest while it's still warm, so if I'm doing a fair bit, I'll break a bit apart using forks, let that cool, break some more apart with a fork, then shread the first bit before it cools too much, repeat.  (so basically, I have one set broken down somewhat to cool faster while I'm shreding an already-cooled off bit).

update as justkt mentioned, the cooking method matters -- roasting and other high heat methods are going to cook the outside faster than the inside.  I typically poach my chicken if I'm going to be shreding it -- bring water to a boil, add chicken, bring back to a boil, turn to low, then leave for an hour or two ... the low temp gets it all nice and tender, while the boiling kills surface bacteria.