In order to make it even more epic, Bethesda has filled Fallout 4 with Exceptional and unique weapons for you to grab and have a more satisfying shooting experience. Take a look at the list below if you want to learn everything about those weapons, how to get them in the Wasteland and their effect on each enemies.
2076 World Series Baseball Bat
It's a reward under Jamaic Plain City Hall. You can sell it to Moe Cronin for a good return in in-game money, if you don't like it. In case you want to use it, you will have a small chance to send targets flying.
Ashmaker
It' a reward for siding with Fahrenheit at the end of “The Big Dig” side quest. It provides you with a chance to light target on fire.
Automatic Laser Musket (Laser Musket)
During the final assault at the start of The Minutemen Quest: The Nuclear Option, you will get this weapon which has a capability of automatic fire.
AX90 Fury (Plasma Gun)
Buy it at Teagan's (The Prydwen), and you'll get 50% more damage vs Super Mutants as an effect.
Wazer Wifle (Laser Gun)
Its best strength is the unlimited ammo capacity. You can get it completing Shaun's three quests once the Main and Faction quests are over.
Wastelander's Friend
Buy it at Deb's at Bunker Hill, and you'll have a weapon with 50% more limb damage.
Virgil's Rifle (Institute Laser Rifle)
Kill Virgil or steal this weapon at his place. This rifle allows you to have 50% more damage against super mutants.
The Last Minute (Gauss rifle)
You will get it at the level 4 workshop merchant. The Last Minute provides you with 50% more limb damage.
Tinker Tom Special (Hunting Rifle)
Sold by Tinker Tom (Railroad HQ), this weapons increases VATS accuracy at the cost of more AP if you are not yet in combat.
Spray 'n' Spray (Submachine gun)
Buy it at Cricket's (caravan trader), and you will get a weapon with bullets exploding on impact doing 15 points area effect damage.
Survivor's Special (Laser gun)
Kill Paladin Brandis or get it as a reward if you convince him to rejoin the Brotherhood in the quest The Lost Patrol. The lower your health is, the more damage you will be able to do.
The Gainer
Solve the Vitale Pumphouse number puzzle, and you will have this weapon setting targets on fire for 15 damage points.
Sentinel's Plasmacaster (Plasma gun)
Reach the rank of Sentinel and Proctor Teagan will sell you this plasma rifle, which doubles damage if the target is at full health.
Shishkebab
It doesn't have any effect unfortunately, but you find it in the Blast Furnace, carried by Slag, with no additional cost.
Shem Drowned's Sword
This weapon provides radiation damage and you get it for free once you complete the side quest The Guilded Grasshopper in the Detective Case Files.
Rockville Slugger
Sold by Moe at Diamond City, this weapon has 40% less Action Point cost.
Reba II (Hunting Rifle)
Barney will reward you this weapon in case you help him in the miscellaneous quest Barney Rook. It makes 50% damage against Mirelurks and bugs.
Reckoning (ripper)
Sold by level 4 workshop merchant, this weapon will allow you to take 15% less damage while standing without moving at all.
Righteous Authority (Laser gun)
This is a reward for completing the quest Call to Arms coming from the Brotherood. It allows you to do double damage with critical shots and fill the critical meter 15% faster.
Lorenzo's Artifact (Gamma gun)
This is a reward for completing Cabot House, and lets you use telekinesis to push targets away.
Old Faithful (Laser gun)
Double the damage if the target is at full health, but unfortunately you will need to pay Arturo at Diamond City in order to have it.
Partystarter (Missile Launcher)
Buy it at KL-E-O's (Goodneighbor): you might need it soon as it does 50% more damage against humans.
Pickman's Blade
Side with Pickman and you will have this weapon which increases damage from sneak attacks and makes targets bleed.
Prototype PA77 (Laser gun)
You will find this laser gun with infinite clip size in the locked safe (Master) inside the University Credit Union.
Railway Rifle
No effects at all, but you can have it free of charges by completing The Railroad Quest: Underground Undercover.
Big Boy (Fat Man)
Buy it at Arturo's (Diamond City) for an additional projectile.
Big Jim (Pipe wrench)
It's lying in Walden Pond, allowing you to have 20% chance to cripple the target's leg.
Broadsider
No effects at all, but you get it free completing the Last Voyage of the U.S.S. Constitution side quest.
Death from Above (Missile Launcher)
This missile launcher is sold by Proctor Teagan after reaching the rank of Paladin. It makes your movements 75% faster while aiming.
Deathclaw Gauntlet
No effects at all, but it comes free as a possible reward for completing The Devil's Due side quest.
Eddie's Peace (.44)
Find it during the side quest Long Time Coming (Detective Case Files), dealing an extra limb damage.
Deliverer
No effects, free after completing the Tradecraft Railroad quest.
Experiment 18-A (Plasma gun)
Fire rate gets 25% faster with this gun, and reload 15% faster. You have to buy it at Institute Requisitions (The Institute).
Final Judgment (Laser Gatling gun)
Fire rate and reload get faster respectively of 25% and 15%. This weapon is carried by Elder Maxson and you will have two chances to steal it from him: during the Institute Quest: Airship Down or The Railroad Quest: Precipice of Wars.
Furious Power Fist
This increases damage after each consecutive hit on the same target. You can get it by removing the thread of Swan in Boston Common.
General Chao's Revenge (Sword)
You can buy this sword at Trudy's (Drumlin Diner) and have 50% more damage against robots.
Good Intentions (laser gun)
This is carried by Gunner leader Clint on the elevated freeway camp, you can get critical hits causing target to frenzy.
Grognak's Axe
Find it in a display case within Hubris Comics, hits cause more stagger and targets take bleed damage.
HalluciGen Gas Grenade
Frenzy targets for 60 seconds with this grenade you can build with the materials you get in the basement laboratory of HalluciGen, Inc.
Homing Beacon (Grenade)
This calls down a missile strike from Zao's sub, it's a reward for completing Side Quest: Here There Be Monsters.
Institute Beacon (Grenade)
Spawns Synths at beacon's location, you get it as a reward for completing The Institute Quest: Airship Down.
Junk Jet
Get it in ArcJet Systems, collect during or after Brotherhood of Steel Quest: Call to Arms.
Justice (Shotgun)
Chance to stagger on hit, you will have to buy it at Penny's (Covenant).
Kellogg's Pistol
It refills your Action Points on a Critical Hit as an effect. Don't forget to get it during Main Quest: Reunions,
Les Fusil Teribles (Shotgun)
As an effect you get +25% damage and limb damage, the con is it has more recoil. You will have to find it in the Captain's cabin in Libertalia.