Here's what stands out in my mind --
Yellow Tang Martini (Polynesian; I think it's on the Ohana menu, but I ordered it in the Tambu Lounge): A combination of butterscotch schnapps, pineapple, and some other stuff. The glass rim was dusted with cinnamon and the drink was sooooooo smooth.
Outer Rim at the Contemporary had a Happiest Celebration drink menu with a cocktail devoted to each Magic Kingdom park. I *think* it was the drink for Hong Kong
Disneyland, but it may have been Tokyo Disneyland. Anyway, it was a fruity cocktail that featured lychee (and was garnished with a lychee).
Wasabi Bloody Mary (Polynesian, Kona Cafe) -- Sure, bloody marys aren't unusual, but this one had an extra horseradish kick and was made with Absolut Pepper. Mmmmmm...
If you visit a (fully stocked) bar and don't find menu items that interest you, don't be afraid to tell the bartender what sort of drinks you like and ask the bartender to recommend a drink. I've found some really tasty drinks that way (peach martini, pez)!