The green-and-gold, spiral-topped tower of this Gothic structure is a Copenhagen landmark, dominating the Christianshavn area. Inside, view a dauntingly elaborate organ from 1698 and the splendid baroque altar, richly adorned with a romp of cherubs and other figures (such as, oddly, elephants). The carillion sounds out on Saturdays at 4pm.

Four hundred vertigo-inducing steps, many of them clambering up wooden ladders in the belfry, will take you to the top of the unique spindled tower. You won't be in a good position to see the spectacular gilded figure of Christ standing on a globe—that's better seen from points away from the building—but you will soak up a panoramic view of the city. Warning: Those steps grow narrower as they reach the pinnacle. In fact, you won't be able to officially summit the structure; the path dwindles into a point, like the Yellow Brick Road, while climbers nervously try to turn around and pass each other in a two-foot-wide space.

A city legend holds that the architect of the steeple, Lauritz de Thurah, hurled himself from it once he saw the builders built the staircase to ascend counter-clockwise rather than clockwise. This, of course, is hooey—he died seven years later, in 1759, after other commissions—but it makes for a nice fable. It is true, however, that you may feel as if you're about to make your own plummet from the spire since it's made of oak that shimmies uncomfortably in stiff winds. It's great fun—and you'll come away feeling like you conquered some fears.

—Jason Cochran