When I was a child (and up to my late teens), most jokes would confuse me. I would take pretty much anything far too seriously and get offended as a result. There were also some puns that were plain disturbing because of the graphic images they gave me, and I failed to understand what could be funny about them. For instance, once, when I was still studying psychology, a friend who was studying said something like, "Oh, hang out your ears /a Russian idiom which means "to pay attention"/ - like, how, on a clothesline with tweezers?" I instantly imagined what she was talking about and just cringed. Then I remember wondering what was supposed to be funny about phrases like this.
In my late teens I gradually learned to recognize the majority of jokes, and came to be amused by them. I also learned to laugh at myself and my shortcomings, which has made life a lot easier.
What makes me wonder though is, there are many types of humor around, and it is also a very culturally dependent thing (i.e., what is funny to a Russian may seem not funny at all to an American, and so forth). It's quite possible to understand only one or a few of those types, and fail to grasp all the others. Sometimes I think that even people who appear to have nosense of humor whatsoever could understand *some* kind of it, out of all that are present in the world.
What seems specific to my personal sense of humor (as with any other visual thinker, probably) is that I am easily amused by phrases that give me vivid images, sometimes the same ones that used to disturb and baffle me before. Sometimes I can be walking down the street and suddenly imagine something unexpected and hilarious, so that I end up grinning like a madwoman and fighting the urge to burst out laughing aloud, and people will look at me funny. This New Year's day, I was with my friend (the same one who made that pun about the clothesline and the ears) at her place, and there was another person with us as well. At some point, I said I wanted to cook some ravioli I had brought, and this person took the saucepan I wanted to use, looked inside and said: "Oh, look, there are potatoes floating in there, - you know, swimming in circles chasing each other" (in Russian, the same word means "to float" and "to swim"). I had this very vivid image of the potatoes swimming energetically in circles, and one of them stopping and gazing at me with these big, black, damp eyes. It was extraordinarily hilarious and I pounded my fist on the table and laughed till I cried. The others were surprised - it was evidently the man's intention to be funny, but neither he nor my friend really expected such a strong reaction from me.