Doughnuts aren't "special" enough, they're often eaten outside of theme parks.
Although I love funnel cakes (with elephant ears not far behind), they're just too big and too messy. So although I might indulge occasionally if I've got friends along to share, my treat of choice is usually a churro. They're very portable, and not so huge and sweet that you end up feeling ill.
More a fair thing than a theme park thing, but my childhood favorite, from the BC era (before churros).