Yes, you CAN tickle YOURSELF! The only place you can tickle yourself is the top of your mouth. TRY IT.
The sensation of tickling is important to have. It's similar to the feeling of having bugs or spiders crawling on you. The reaction you have to being tickled is important to keep those kind of animals from crawling on you.
You tickle mostly because of surprise. Even if you know you're about to be tickled, you don't necessarily know where, so you react by being ticklish. When you try to tickle yourself, it usually doesn't work because your brain already knows how you're going to do it. You can't tickle yourself because you can't surprise yourself.
Possibly because the roof of your mouth isn't used to being touched like that, it still tickles if you touch the roof of your mouth.