Maybe not the most inspired list, but these are some that jumped to my mind, then a few that came up as I typed out the list. Like usual, these are a bit subjective. I reserve the right to steal good suggestions from other lists.
Luke's/Anakin's Lightsaber (Star Wars)
Conan's Atlantean Sword (Conan)
He-Man's Power Sword (He-Man and the MotU)
Lion-O's Sword of Omens (ThunderCats)
Connor McLeod's Katana (Highlander)
Logan's Claws (any X-Men/Wolverine/Logan cartoon or movie)
Bilbo's/Frodo's Sting; although pretty much all of the Weta swords in the movies are cool looking. (Lord of the Rings)
Darth Maul's Double-bladed Lightsaber (Star Wars: TPM)
Thor's Mjolnir (Thor and Avengers movies)
Captain America's Shield (Captain America and Avengers movies)
Some Honorable Mentions:
Excalibur (Excalibur); Voltron's Blazing Sword (Voltron); Did I mention pretty much any sword from LotR?; Gimli's "Walking" Axe (LotR); Aang's Glider-staff (AtLA); Blade's Sword (Blade); Samurai Jack's Katana; Hattori Hanzo Katana (Kill Bill); Mizu's Katana (Blue Eye Samurai), Galen's Spear (Dragonslayer), Perseus's Divine Sword (Clash of the Titans 80s)