It is possible to (sort of) tickle yourself, try lightly stoking the middle of the roof of your mouth. Careful though you could Involuntarily bite your finger.

It is an uncontrollable response, so there!

My eight year old son will laugh uncontrollably if I put my hand close to his bare foot. I don't even have to touch him (although I'm holding his foot with my other hand). Try to explain that one, folks.