Unique Weapons are special weapons that can be found or acquired in Skyrim. The weapons can be found during exploration or as part of a specific quest. There are currently 80 known unique weapons. Each of the weapons has a unique name and/or special properties which set it apart from other weapons of that type. Some of these weapons' damage scale according to the level they are acquired.
Blade of Woe - Unique dagger given to the player at the end of the Dark Brotherhood questline from Astrid or by killing Astrid in the beginning of the With Friends Like These... quest. Absorbs 10 points of health from the target. The Blade of Woe can also be pickpocketed from Astrid at any time before starting the quest To Kill An Empire. In order to do so, the player must have a pickpocketing skill of at least 70 and the associated perk Misdirection. Thus, it is possible to obtain two Blades of Woe.
Borvir's Dagger - Found next to Borvir's body outside the entrance of Journeyman's Nook. Not enchanted. Has identical damage and weight of an Elven Dagger.
Kahvozein's Fang - Used to obtain Dragon Heartscales needed to unlock the Master level Alteration spells.
Keening - Received at the end of the quest Arniel's Endeavor. Absorbs 10 health, stamina and magicka from the target. Can't be recharged.
Rundi's Dagger - Found on an unmarked location on the map on small shrine between Winterhold and Journeyman's Nook. There are frost traps so it's best to approach from the rear.
Shiv - Possible to obtain during the quest No-one Escapes Cidhna Mine. Has a unique look but no extra effects and mediocre damage.
Chillrend - A unique Glass Sword found in a display case in the basement of Riftweald Manor in Riften. Deals a level-dependent amount of frost damage and has a chance to paralyze the enemy.
Dawnbreaker- Daedric artifact of Meridia. One-handed sword. Given to the player upon completion of The Break of Dawn. Deals additional fire damage, and upon killing an undead foe, has a chance to cause an explosion dealing damage and causing Fear to all undead nearby.
Ghostblade - It is located at Ansilvund Excavation, after defeating the mage Lu'ah Al-Skaven. Deals 3 points of extra damage, ignoring armor. Has a weight of 1 with base damage of 9. (Upgraded using 3 Ectoplasm)
Grimsever - One-handed Glass sword belonging to Mjoll the Lioness. Retrieving this sword from Mzinchaleft is the objective of her quest to obtain her as a follower. The sword can be retrieved from her inventory after the quest is complete. Deals frost and stamina damage.
Red Eagle's Fury / Red Eagle's Bane - Red Eagle's Fury is obtained at the Sundered Towers, and deals additional fire damage. Taking the sword to Red Eagle's Tomb in Rebel's Cairn allows you to complete a misc. quest to upgrade it to Red Eagle's Bane, which has higher base damage and causes Turn Undead in addition to the fire damage.
Balgruuf's Greatsword - Unique Steel Greatsword, Quest Item given by Adrianne in Whiterun to be delivered to her father, Proventus, Advisor to Jarl Balgruuf the Greater as part of a misc quest.
Ebony Blade - Daedric artifact of Mephala. Reward for completing the quest The Whispering Door. You can increase its damage by using it to murder NPCs with a high disposition towards you. Achieves it's maximum damage after ten murders. Once fully charged, targets will not treat attacks with this weapon as assault. Onlookers will, however. NOTE: This weapon's damage is modified by relevant Two-Handed perks. However, the weapon's damage is increased by your overall One-Handed skill, rather than your overall Two-Handed skill, so this blade will not be effective in the hands of a pure Two-Handed weapon user.
Headman's Axe - Wielded by Ahtar, a possible follower. It's not enchanted.
The Longhammer - A unique Orcish warhammer found in Liar's Retreat on a table near a dead NPC in the final room of the dungeon. Swings 30% faster than a normal warhammer.
Rueful Axe - Two-handed axe. Possible reward from the Daedric quest A Daedra's Best Friend, but does not count as a Daedric artifact. Deals additional Stamina damage. NOTE: This weapon has one of the slowest swing speeds in the game.
Trollsbane - A unique steel warhammer found on the body of Frofnir Trollsbane in the mountains of The Reach. Deals additional fire damage to Trolls.
Volendrung - Daedric artifact of Malacath. Warhammer obtained for completing The Cursed Tribe. Absorbs stamina, and swings slightly faster than a usual warhammer.
The Woodsman's Friend - Two-handed axe. Found north of Pinewatch next to a dead woodsman and a tree. It is not on the woodsman's corpse but on the ground beside him. It is quite easy to miss. It is not enchanted. Just south of the enchanter's altar.
Wuuthrad - A unique battleaxe received at the end of the Companions questline. Bears the tag "Especially deadly to elves.". This gives the axe a +20% damage rating against Altmer, Bosmer, and Dunmer. It will not, however, confer a damage bonus against Orsimer or Falmer.
Eye of Melka - Unique staff found in Four Skull Lookout's attached cave. NOTE: This location changes based on your level and whether or not you have cleared certain dungeons. Agree to assist Melka, the Hagraven you meet at the start, and she will reward you with this at the end. Causes a fiery explosion, damage is levelled to your character.
Skull of Corruption - Daedric artifact of Vaermina. Possible reward from the quest Waking Nightmare. Deals additional damage if charged with dreams, which can be collected from sleeping NPCs.