Ticklishness is in your head. That is, the sensation happens when you are not expecting to be touched, or when someone's touch is unpredictable. The first part (reacting strongly when something touches you lightly and you're not expecting it) is a response we've adapted to protect ourselves against creepy crawlies, or even predators. Think of the fear you have when you're hiking and something brushes the back of your neck. That could be a snake on a tree branch ready to strike, or a poisonous spider that just crawled down your shirt. Think also of the fear you have when someone taps your shoulder unexpectedly. That person behind you, whom you didn't know was there, could have been a mountain lion stalking you, ready to strike. The sensation of a light touch or a surprising touch is slightly fearful and that fear causes us to laugh (believe it or not). The second part (reacting strongly when someone touches you in a sensitive spot even though you know they are going to touch you) is also due to fear: fear of the unexpected. Sensitive spots are often vulnerable spots: the belly, which houses some important organs; the feet and the knees, which we need to run away from predators; the neck, which is so easily damaged and houses our arteries; or our armpits, which also house important arteries. Usually when someone tickles you they are a friend, and you know they're not going to harm you. But their touch is unpredictable, and just the smallest bit of fear that they could harm you makes you react strongly to their touch. So it makes sense that you can't tickle yourself, since you know where you are going to touch yourself, when you'll do it and exactly what you'll do next. Your brain anticipates the touch and there's no surprise and no fear. I am so ticklish that I CAN tickle myself if the touch is light enough and on a sensitive spot (underarms, feet). And I can't stand anyone touching my feet. Valerie Franck

That's a great question.If we laugh when someone else tickles us, it seems to make sense that we could tickle ourselves, but I've never known anyone who could. I found an interesting explanation at this site:
how stuff works

Basically, there are three important things going on:
1. Our bodies filter out unimportant information.
Your body constantly gets messages about things touching you. Your clothes touch you, your feet may touch the floor or your body touches a chair. Your brain ignores this information most of the time so that you can concentrate on important things.

Bugs crawling on you have a very light touch, so normally they might not get much reaction from our brains. It might be very important to know that there's a bug on you, so maybe that's why we evolved a tickling sensation that we really pay attention to. If someone tickles you, you try to escape or get rid of it. Maybe the tickling response makes us try to get rid of spiders, ticks, or insects that might be dangerous.

2. Our brains pay more attention to surprising things.
If you are reading or watching TV and scratch your nose, you probably won't even remember doing it. But if your friend scratched your nose, you'd be surprised and remember that.

When you tickle yourself, there's no surprise. Your brain knows you're going to try tickle yourself because it gives the orders to your hand. So it doesn't pay much attention. If you touch the soles of your feet, You feel yourself touching your feet, but there's no tickling sensation.

There's an interesting experiment that showed how important surprise is. If people use a robot to tickle themselves, they do laugh. The important difference is that there's a very small pause between the person starting the robot and the robot starting the tickling, so even though they are expecting to be tickled, their brain is fooled because the touch doesn't happen when the signal to move the hand is sent out.

3. We sometimes laugh when we are scared or uncomfortable.
According to the site I looked at, laughing is a response to a person being scared or uncomfortable about being tickled. If your brain knows that you're the one doing the tickling, there's no fear involved, so you don't "feel tickled." I don't know why some kinds of fear make us laugh and some don't, or why some spots are more ticklish than others.

If tickling is really part of a bug-avoidance system, we would expect other animals to be ticklish. Do you think they are?Thanks for asking,

I think that tickling, as it is usually practiced, has two components. There is the reaction to the actual touch sensation from body parts that are not usually touched in a certain way. There, I think the observation is actually wrong: One can in fact tickle oneself. Feathering the sole of my foot myself gets me to the verge of laughing. But there is a much larger behavioral and psychological component to it. Besides the physical aspect of it, it is a form of interpersonal or social interaction. (It would be interesting to know whether other primates tickle each other.) As a social species, we are probably hardwired to enjoy this kind of interaction. Without a partner, it obviously won't work.