Katanas and rapiers
Undoubtedly due to the ever-increasing fraction of otaku and other japanophiles in the general US population, in popular culture katanas have now acquired the status of the ultimate cold-steel weapon. (See Kill Bill for concrete examples.) Claims of the katana’s superiority naturally draw the righteous anger of fans of other swords. For example, consider this /. post and the discussion that follows it, or this theoretical description of a knight vs. samurai showdown.
I am not a historian, so I cannot judge whether katanas became popular before or after the obsolescense of armor, or whether the yumi, the yari, or the tachi was considered to be the soul of 15th century samurai. However, I have always found it unbelievable that a light sword obviously designed for draw cuts would do much against good metal armor (or cars, aircraft, trees, tanks, large buildings, and other objects that popular fiction portrays as katana-cuttable). To pierce armor, Europeans used longbows, crossbows, guns, pikes, lances, and (I think) specialized armor-piercing daggers; or they just bashed at the armor with a mace or a morningstar. Swords were for use against softer targets.
On a similar note, there is an excellent analysis of a fight between unarmored opponents, one armed with a katana, the other with a rapier. The major issues are that a katana hit on an unarmored body is lethal, and a rapier isn’t strong enought to block a katana; on the other hand, a rapier has longer range than a katana, and a katana is too slow to block a rapier strike. The basic conclusion is that at any point in the fight, the katana-wielder could go for an all-out attack resulting in the immediate deaths of both opponents; however, wielding the katana purely defensively would let the rapier-wielder make enough small holes in the samurai to eventually win.