There are many that surprise me as not being more common. Namely the back, shoulders, and lower legs. But I don't really think of it in a way where I keep a mental list of spots. Sure, I know where people are more likely to be ticklish, but I more enjoy exploring and finding out on the individual. I find that if I go in with no pre-conceived ideas, it's much more likely that both of us will be surprised, and it is much more fun! Ticklish people seem to be ticklish in more areas than most people, including them, would expect.
For anyone who hasn't deviated much from the typical spots, I'd suggest first trying all the limb joints: the ankle, wrist, knee, elbow, shoulder, and hip. Additionally, one thing that I keep in mind is that sensitivity varies, not only from day to day, but from spot to spot. For example, my wife is one big tickle spot, but different parts of her body are more or less ticklish different days. Today her tummy might be a little ticklish and her back terribly ticklish, though tomorrow, those might be noticeably reversed. All the better reason to stick with the no-assumptions exploration.
In terms of techniques, each tickles different people differently, so if you try something and it didn't work quite so well, don't dismiss it entirely. For a long time, I thought feathers were more of an overhyped, underperforming tool that were best left to conceptual symbolism rather than for practical use, but some people are so sensitive that even a feather will drive them crazy. I've come to accept that as the beauty of the feather as a tool in saying this person is so ticklish that even a feather can tickle them silly. I think one technique that is more frequently overlooked is more often switching between hard and soft tickling. The mind tries to get used to uncomfortable things quickly to cope. If you're tickling someone's ribs with hard tickling, it can be amazing how much they jump when you switch to soft tickling in the same area. It took me a while to figure that out. People tend to think start soft and move harder and harder, because harder is more intense, but that's not always how it works. What I try to do is switch between the two as I notice the lee beginning to get used to it. Another is quickly switching between different spots. They never get time to get used to it and most lose control quickly, falling into a tickle panic.