If you're still looking for actual mythological names, I'll give you a couple of them:
Durandal/Durendal: The sword of the paladin Roland. Utterly indestructable.
Lævateinn: Sword from Norse Mythology.
Tyrfing: Another Norse Mythos sword. It never misses a stroke, will never rust and cuts through metal and stone as easily as cloth, but is cursed to kill a man whenever it is drawn and to be the cause for three great evils.
Gram: The sword Siegfried/Sigurðr used to slay Fáfnir.
The Lance of Longinus: Longinus was the centurion assigned to stabbing Jesus with a spear to make sure he was dead, so this is a spear that killed a god, at least metaphorically.
Kusanagi no Tsurugi: Found in the body of the Yamata no Orochi, it can control the wind.
The Sampo: From Finnish mythology, it is never stated what it is, but it can produce both salt and gold, and presumably much more.
Arondight: Sword of Lancelot, one of the Knights of the Round Table. That's about it.
Spear of Lugh/Areadbhar: From Irish mythology, it is a living spear that moves on its own and has a near-insatiable lust for blood and battle. It basically had to be kept sedated between battles.
Sword of Light/Claíomh Solais: Another Irish thing, it's a sword that shines like a torch. Once drawn, no-one could escape or resist it.
Cauldron of Dagda: Since I've mentioned half of the jewels of the Tuatha Dé Danann, let's continue. The Cauldron of Dagda is bottomless and never ran out of food.
Stone of Destiny/Lia Fáil: When the rightful king of Ireland puts its foot upon it, it will roar out. It can also rejuvenate said king.
Other stuff that involved Jesus: The cross, the nails in said cross, the holy grail, the shroud of Turin, the crown of thorns, I can't be arsed to describe any more stuff.
Anyway, I need to go to sleep now. Hopefully this will help.