What is ticklishness?
Having thought and read about your question for years, I offer some thoughts:
There have been many theories, beginning in about the 19th century, for ticklishness and the laughter it (so wonderfully) produces. They range from an evolutionary defensive reaction against insects crawling on your skin to a process for encouraging bonding between mothers and children. Some of these theories do not explain the laughter component at all.
However, the theory that really seems to fit best first became known to me in the new edition of the Encylopaedia Britannica. The term they coined for it is "bissociation". In my own words the concept they describe is this: Tickling is a kind of playful attack which causes the recipient to experience two different strong emotions at once. On the one hand, she or he is being "attacked" which creates some fear or anxiety, but at the same time, the ticklee knows it is not for "real", that the tickler is not really trying to hurt her or him. This living on two contradictory levels at once generates laughter as a release.
In this way tickling is like a lot of verbal humor where a joke gets you to temporarily accept a reality which you know deep down couldn't be. For example, the classic case of chutzpah about the man who kills both his parents, but throws himself on the mercy of the court because, after all, he is an orphan.
On the one hand, this is completely ridiculous, but at the same time the man's behavior follows the logic of courtroom practice and his claim is "true".
This bissociation theory shows that ticklishness is mainly psychological and it explains so much about the dynamics of tickling. Being ticklish does depend on the "ability" of the tickled person to perceive the touches as a (mock) attack. Some people will just never feel that having fingers moving around on the bottoms of their feet could really "get them". But the same person having one little pinky move closer and closer to her ribs or underarms could really feel "threatened" and out of control.
On the other hand if the tickled person doesn't feel that she or he is (ultimately) safe and won't really be hurt, the tickling is much more likely to be experienced as painful. This also explains why some people cannot stand to be tickled or scream rather than laugh: they can't feel that the touching is in fun and go with it--it is just too threatening.
Control, or lack of it, is a key element. If you feel perfectly in control there is no threat, not even a playful one. This is why a lot of people say "I'm not ticklish, unless someone tickles me by surprise". It is not the "surprise" that makes them ticklish, it is that they were off guard and felt more vulnerable. Now they can sense the "attack".
Finally--and I'm sorry if this is too long for many of you--the fact that ticklishness is part of a psychological "contest" is reflected in this: Many people are not so ticklish if they feel they can "get away" from the tickler whenever they want, but if they are "trapped" or "in your power", they go crazy. In other words, the very same physical sensations are experienced in very different ways emotionally.
By the way, I feel that understanding the tickling dynamic does not take away from, but rather enhances my appreciation of tickling's many pleasures.
Thanks for listening.