My fiance is Chinese and she absolutely loves chicken feet. They are quite big in Guangdong province China. As someone else mentioned, a common dim sum dish. I'm not such a big fan.

Duck Blood Soup - Tried this in Chongqing China. Actually very spicy and pretty good flavor.

Pig Stomach - Another dim sum dish, not bad, but a weird texture.

Fish Eyes - Another one that I'm not greatly enamored of.

Preserved Eggs - Perhaps not the strangest, but the burying them in straw to ferment seemed strange to me. The ones I had were in some sort of liquid. Very strong taste. Good, but I didn't eat too many.

And a huge second to the scorpions in Beijing. They have everything there! From grubs, to grasshoppers, to starfish, snakes, you name it. I've never seen anything like it before!