Here you can find a list of all of the unique weapons (and sometimes armor) in Fallout 4. Unique weapons are far and away much more numerous than unique armors are, but if its rare and not randomly dropped you can find it here!
Note: In-depth detail about the damage , weight, speed and value of these items isn't provided in this section. This is because much of it is dependant on IF you have any perks leveled (which affects the damage) and if you modify it at all (which can affect multiple things). Almost all unique items can be upgraded like any regular item, so aim for the upgrades you want regardless! These items are listed in alphabetical order.
2076 World Series Baseball Bat
Unique Effect: Small chance to send targets flying.
Found: This wooden bat is one of the rewards at the end of the "The Treasures of Jamaica Plain" miscellaneous quest.
Alien Blaster Pistol
Unique Effect: N/A (Unique Weapon)
Found: Found on the body of an Alien! No kidding! Search east of Oberland Station (southwest of Diamond City) and follow the "Garbled Radio Signal" to find the alien. Kill it for this weapon. Note that you can mod it and it uses special "Alien Blaster" ammo, which the alien also drops.
Unique Effect: Sets target on fire for 15 points of damage.
Found: Quest reward for "The Big Dig" in Goodneighbor (you can get this no matter which side you pick... even off of a corpse if needed).
Unique Effect: Shoots an additional projectile.
Found: This is a rare unique Fat Man, one that shoots multiple mini nukes. Crazy and expensive! You can buy it from Arturo in Diamond City.
Unique Effect: 25% chance to cripple the target's leg.
Found: This unique wrench (which is very rare) is found at Walden Pond, in the work room full or Raiders on a shelf (inside the drainage pipe area).
Unique Effect: N/A (This thing fires cannonballs!).
Found: This unique cannon-like weapon has high damage and actually fires cannonballs. Just... wow. This is a quest reward from Captain Ironsides when you do the quest "Last Voyage of the U.S.S. Constitution" .
Unique Effect: N/A (Freezes Enemies)
Found: Inside Vault 111, in a [MASTER] locked case by the exit. You can pick it or have Dogmeat retrieve it. So cheap!
Death From Above
Unique Effect: 75% faster movement while aiming.
Found: This missile launcher is sold in the Prydwen Shop. Not a very impressive unique effect, especially given its price...
Unique Effect: N/A (Unique Unarmed Weapon)
Found: You can find this unique unarmed weapon while doing the side quest "The Devil's Due" , which begins in the town of Salem (in the northeast portion of the map). You can take either side and still pick this up as long as you visit the Deathclaw's Nest.
Unique Effect: Improved VATS hit chance, 25% less Action Point cost.
Found: Found during the Railroad Quest "Tradecraft" . Can't miss it!
Unique Effect: 50% more limb damage.
Found: Complete Nick Valentine's personal quest "Long Time Coming" . Eddie will drop this .44 on the ground once you (or Nick) take him out. It won't be in his inventory, so be sure to pick it up.
Unique Effect: 25% faster fire rate, 15% faster reload.
Found: This unique plasma rifle is sold at The Institute store (bring a good chunk of caps with you).
Unique Effect: 25% faster fire rate, 15% faster reload.
Found: This unique weapon is a Gatling Laser gun, and is Elder Maxson's personal weapon (the Brotherhood of Steel leader). You can acquire it if you make them your enemies and pick it up off his corpse.
Freefall Armor (Left and Right Leg)
Unique Effect: Prevents falling damage (with Right Leg).
Found: Now this armor is a pain to get. You must have a jetpack on your Power Armor, which is likely to come late in the game which is also good as you need to have cleared the "Mass Fusion" building in the main story missions as well. With those two things done, head to Mass Fusion and take the right elevator and then the left elevator up to floor 8. Now, you must use the jetpack to leap from broken ledge to broken ledge for about 7-8 floors until there are no more ledges. Now here you want to quicksave and then look to the south/southeast corner. Up above on the south wall is a room... you need to jet to that, but your jetpack won't last that long. The trick is to try to wedge into the south/southeast corner while taking Jet and Nuka Cola Quantum (for the AP), and boost yourself up there. This is hard (thus the quicksave), but with a few tries you can do it. This room has a Fusion Core in it. Quicksave again as you must do another hard jet section. From the hole, you need to jetpack to the northeast corner. Once again, try to wedge yourself in the corner and if you get caught let yourself regain AP. Use Jet and Nuka Cola Quantum to head upwards and enter the office you find on your right. Inside this office is a [NOVICE] safe with the armor set inside. Congrats!
Furious Power Fist
Unique Effect: Increased damage after each consecutive hit on the same target.
Found: This is found on the body of the Super Mutant Behemoth "Swan" at "Swan's Pond", east of Diamond City.
General Chaos Revenge
Unique Effect: Does 50% more damage against robots.
Found: Sold by Trudy at the Drumlin Diner, southeast of Sanctuary. Note that you must not kill her in the standoff with Wolfgang in order to buy this weapon from her.
Unique Effect: Critical hits cause target to frenzy.
Found: This awesome-sounding weapon (Cell-Based) is found on Clint, the unique Gunner boss located in the Quincy Ruins in the southeast portion of the map.
Unique Effect: Hits cause more stagger, and targets take bleed damage.
Found: This can be found at Hubris Comics (northeast of Diamond City), inside a locked display case. Very good early melee weapon, for sure.
Unique Effect: Increases the wearer's strength and melee damage.
Found: This item can be found on the top floor of Hubris Comics (northeast of Diamond City). Inside an open locker, so look carefully.
Unique Effect: Increses Action Point refresh speed.
Found: Bought from the Brotherhood of Steel shop on the Prydwen.
Unique Effect: N/A (Shoots random junk from your inventory).
Found: This odd and unique weapon is found in Arc Jet Systems (Arcjet Engine Core) during the Brotherhood of Steel quest "Call to Arms" .
Unique Effect: Chance to stagger on hit.
Found: This unique shotgun can be bought off the merchant at Covenant (which is north of Diamond City / northeast of Lexington).
Unique Effect: N/A - (Decent armor if you are rushing the story...).
Found: It belonged to Kellogg. Not that he needs it anymore! Yours after completing the main mission quest "Reunions" .
Unique Effect: Refills your Action Points on a Critical Hit.
Found: It belongs to Kellogg, of course! You can, um... "borrow" it from him after completing the main mission quest "Reunions" .
Unique Effect: Targets bleed and are poisoned. Exceptional damage.
Found: You can find this item when you explore the Dunwich Borers location, just southwest of Salem (in the northeast portion of the map).
Le Fusil Terribles
Unique Effect: +25% damage and limb damage, but has more recoil.
Found: Best done during the quest "Synth Retention" as it is on the way, but can be found at Libertalia on the east side of the map (east-center), up in the tallest ship in the Captain's cabin.
Unique Effect: N/A (1 CHR, Unique Look).
Found: You must complete the quest "Last Voyage of the U.S.S. Constitution" while siding with Captain Ironsides.
Lorenzos Artifact Gun
Unique Effect: N/A (has a unique mod that knocks back enemies, but is similar to a Gamma Gun).
Found: Found when doing the quest "The Secret of Cabot House" . Note that you must side with Jack at the end to obtain it, as well as give him a short amount of time to make it for you once the quest is done.
Unique Effect: N/A (Good CHR item, Unique Look)
Found: You can get this suit (which is an OK CHR item - but not the best) by doing the quest "The Secret of Cabot House" .