It is strange we laugh when someone tickles us. Laughter usually signals enjoyment, yet I generally want people to stop tickling me. So I did some brief research. I emphasize brief.
Laughing when another person tickles you is a natural reaction. Scientists have discovered that the feeling experienced when we are tickled causes us to panic and is a natural defense to little creepy crawlers like spiders and bugs. Slight tickles from insects can send a chill through your body letting you know something is crawling on you.
That same ticklish feeling sends us into a state of panic and elicits a response of uncontrollable laughter if a person tickles us. It's the moment that you least expect to be tickled and are that causes you to feel extremely uneasy and panicked, which leads to the most intense ticklish feeling. Even if you do know that you are about to be tickled, the fear and unease of someone touching and possibly hurting you causes you to laugh. Some people are so ticklish that they begin laughing even before they are touched.
So, if someone else's touch can tickle us, why can't we tickle ourselves? Much of the explanation for this question is still unknown, but research has shown that the brain is trained to know what to feel when a person moves or performs any function. We aren't aware of a lot of the sensations generated by our movements. For example, you probably don't pay much attention to your vocal cords when you speak. For the same reason, we can't tickle ourselves. If we grab our sides in an attempt to tickle ourselves, our brain anticipates this contact from the hands and prepares itself for it. By taking away the feeling of unease and panic, the body no longer responds the same as it would if someone else were to tickle us.
— From How Stuff Works