Angelic weapons are implements belonging to Heaven that are imbued with some supernatural power. The most common is the angel blade. Following the imprisonment of Michael and Lucifer in Lucifer's Cage, a civil war takes place in Heaven. A collection of powerful weapons from Heaven's armory disappear, and are then sought by rival factions of angels. Later, Lucifer seeks out especially strong heavenly weapons that may be on Earth in order to stop the Darkness.
Castiel: Before the Apocalypse, Heaven may have been corrupt, but it was stable. The staff was safely contained. It's been chaos up there since the war ended. In that confusion, a number of powerful weapons were stolen.
Dean: Wait, you -- you're saying your nukes are loose?Castiel: Yeah, I'm afraid so.
In the battle between angels to control Heaven, Castiel says "Whoever has the weapons wins the war." Raphael wants the weapons so he can take control of Heaven and restart the Apocalypse. It is discovered that Balthazar stole the weapons, and wants them for his own unstated ends. He uses a portion of one weapon to buy a human soul, and destroys Raphael's first vessel with another. Eventually Balthazar decides to turn the weapons over to Castiel. Castiel confirms to Raphael at their next confrontation that he has the weapons, which forces Raphael to flee.
This short, silver blade can wound and kill angels. Multiple blades exist, and by season five most angels carry them. It has been shown that humans and demons are capable of effectively wielding them as well and they are deadly to angels, demons, hellhounds, reapers, and nephilim.
Castiel tells Sam and Dean there is a weapon that will kill Fate. Balthazar appears behind Atropos with a blade but Castiel stays his hand. The weapon appears similar to an angel sword although the blade is more rapier-like in shape, and it is golden in color.
Sam pretends to have found the Ark of the Covenant as a ruse to get Castiel to help him and Dean. Later on in the series, Dean witnesses a piece of the actual Ark of the Covenant being found and used.  The Ark is considered a Hand of God.
This is a subclass of heavenly weapons. According to Lucifer, these weapons are objects on Earth that were directly touched by God and imbued with God's power, though most were believed to have been destroyed due to their instability. Mortals cannot survive touching these objects, and the power of the object can only be used once before it's depleted. Hands of God have been used by Delphine with the Ark of the Covenant and by Crowley with the Rod of Aaron.
When people start being compelled to tell the truth, Dean and Castiel suspect that it made be caused by Gabriel's Horn of Truth. However the Horn is not found in the city, and the culprit is revealed to be the goddess Veritas.
A lance which once belonged to Michael, for the purpose of defeating Lucifer. It has the power to turn quickly any demons into dust, and conversely causes angels to essentially rot away, dying slow and agonizing deaths.
This crystal turns a human body to salt.
A spear stored by Lucifer in one of his crypts and retrieved by demons after he reclaims Hell. Lucifer later wields his spear in battle against the Darkness, impaling her through the back with it after she is struck by witches, angels and demons. Lucifer's spear is able to defeat Amara in her weakened state.
Given to Moses's brother Aaron by God, the rod is considered a Hand of God and is capable of incredible destructive power. It was sought out by Lucifer during his search for weapons to defeat the Darkness, but was used by Crowley in a failed gambit to kill Lucifer. Crowley described holding it as, "So this is what it feels like to be God," and seemed to suffer no negative side effects from its use, although after attacking Lucifer its power was dissipated. 
Sword of Michael
At first, it seemed that the "Sword of Michael" was an actual angelic weapon which Michael used to defeat Lucifer, but it is later revealed by Zachariah that Dean Winchester is in fact the "Michael's Sword" - Michael's true vessel.