The idea of a weak spot can also apply to monsters, such as Tolkien's dragon Smaug. Tolkien was quite familiar with Norse mythology, and so presumably would have been aware of both Siegfried's own weak spot and the fact that the hero killed Fafnir in dragon form by stabbing him in the belly. Although the Death Star isn't a living thing, its destruction by exploiting a weak point is accomplished in much the same manner. And sometimes it isn't a body part that is vulnerable, but rather a particular method of killing that has to be used. Examples include the various means of killing vampires (a stake through the heart being the most popular, but far from the only one), silver for werewolves, Kryptonite for Superman, and water for the Wicked Witch of the West. (In fairness, L. Frank Baum never said the Witch was otherwise indestructible, and in fact she probably wasn't, but I'd still say it counts.)
Another variation of the theme came to mind during my reading of Lloyd Alexander's Taran Wanderer. The evil wizard Morda traps his life force in his little finger, which he cuts off and hides. This is the same basic idea as what Voldemort did with his Horcruxes, and it shows up in other stories as well. Heck, even Paper Mario uses that same basic concept with Tubba Blubba's heart.
In some of these cases, it seems like it was only something minor that stopped these characters from being totally invulnerable. For instance, if Siegfried had just thought to check his body for leaves, he wouldn't have HAD the weak spot. But I think there's a little more to it than that. It's a general rule in stories that involve magic that none of it can be absolute. Every spell has its counterspell, every curse has its loophole, and everyone who's otherwise invincible has to have a weakness.