I think the soles are appealing because there is a softness and innocence to them. There is a great contrast between the soles and tops of the feet, too. The tops are often bony and muscular, and the soles are vulnerable, ticklish, and sensitive. Also, because of the taboo nature of feet, especially the soles (a lot of people don't welcome the sight of them unless it's an appropriate place like the beach), there's something naked about them, and it's often humiliating to have them exposed or seen. They're a very private part of the body for many people, and this goes well with the interest in tickling them. It's like double the humiliation for the person.
Finally, the sole represents the image of the foot that most people think of. It's the shape of footprints, the logo for a business (perhaps a footwear company), or a design feature on clothes or accessories. Our fascination with them starts from birth: ever seen those new baby footprints cards? It's such a universal symbol, and the best symbols are the ones you can easily recognize, draw, or recall. Soles are simply special.