While it is possible to get every unique weapon in Fallout 3, it requires lots of forethought, some of which starts right when your in Vault 101. The following are the unique weapons that require the forethought; Plunkett's Valid Points, Ant's Sting, Butch's Toothpick, Callahan's Magnum (Broken Steel), Paulson's Revolver (Mothership Zeta), Sydney's 10mm "Ultra" SMG, A3-21's Plasma Rifle, Atomic Pulverizer (Mothership Zeta), MPLX Novasurge and Protectron's Gaze.
To obtain Plunkett's Valid Points, the unique Spiked Knuckles, you must get the Lawbringer perk. Junders Plunkett will spawn in the Arlington House once you have the perk, allowing you to kill him and take his Valid Points.
To acquire both the Ant's Sting(a unique Knife)and Protectron's Gaze(a unique Laser Pistol), you must get a hold of 2 kinds of Raider armor (any kind works). Activate the Superhuman Gambit quest and run to the AntAgonizer's Lair. Once in the throne room, reverse-pickpocket the raider armor onto the AntAgonizer (this usually requires a high Sneak skill). Exit the throne room and re-enter. She will be wearing the Raider armor now and you can now pickpocket her attire off of her person. Give the AntAgonizer's armor to the Mechanist and he will reward you with the Protectron's Gaze. You can then reverse-pickpocket the other Raider armor into his inventory. Leave his lair and return. He should be wearing the armor. Pickpocket the Mechanist's armor out of his inventory ( you can also take back the AntAgonizers armor too. After all, it is a collector's item.) If you don't mind if the Mechanist is dead, you can also kill him and obtain his armor that way. For an ironic twist, you can kill him with the Protectrons Gaze. Either way, return to the AntAgonizers Lair and give her the Mechanist's armor. She will reward you with the Ant's Sting.
To get hold of Butch's Toothpick, the unique Switchblade, you cannot kill Butch in Vault 101 during "Escape!". Leave him alive so he will still be in Vault 101 during "Trouble On the Home Front". When talking to him, you can convince him to leave the Vault and head for Rivet City. Here, he will stay in the Muddy Rudder Bar until you ask for him to come along with you as a follower. You must have neutral karma to have him as a follower. Once he is your follower, you can go into his inventory and you can get the Toothpick.
To gain Callahan's Magnum, a unique Scoped .44 Magnum, you must destroy the Citadel. In the crater that used to be the Citadel, there is a door into the Armory. Inside the armory are lots of goodies, like a Mini Nuke, Nuka Grenades, Alien Power Cells, and of course, Callahan's Magnum. Be careful though; destroying the Citadel makes you miss out on TONS of caps and XP. By NOT destroying the Citadel, you can turn in Cameras for 100 caps and Sensor Modules for 75 caps to Scribe Rothchild. Also, you can give to Paladin Tristan Super Mutant Blood Samples for 50 caps and 10 XP each. So you have to make the tough decision to get Callahan's Magnum or get loads of caps and XP.
To attain Paulson's Revolver, Paulson must be killed. Either from alien gunfire or yours, it doesn't matter how he is killed. You cannot pickpocket the revolver off of Paulson's person; only upon death is the revolver on his inventory.
To obtain Sydney's 10mm "Ultra" SMG, the unique 10 mm SMG, you have to simply meet Sydney in the National Archives. You can, like above, kill her yourself or wait for Super Mutants to gun her down. I recommend keeping Sydney alive because after the quest, she will head to Underworld where she sells TONS of ammo to you. But if you keep her alive, she will not automatically give you her SMG. You will have to find the note "A Note from Little Moonbeams Father ". If you mention this note to here, she will give you the SMG and realize her father wasn't a piece of trash.
To acquire A3-21's Plasma Rifle, the unique Plasma Rifle, you must tell Harkness in Rivet City that he is an android. This speech option does not show up until you have spoken to Pinkerton. By not ratting Harkness out to Zimmerman, Harkness(A3-21) will give you his plasma rifle.
To get hold of the Atomic Pulverizer, the unique Alien Atomizer, YOU MUST HAVE A SCIENCE SKILL OF 75. Without this skill you cannot open a door near the entrance to the Weapons Lab on the right. Once inside this room, it on a rack to the right, next to a normal Alien Atomizer.
To gain the MPLX Nova Surge, the only unique Plasma Pistol, to must also have a science skill of 75. In the Cargo Hold of Mothership Zeta, there is a functional computer. By hacking your way through, you can remotely unlock a safe near the garbage chute with a mechanical claw dropping waste into the aforementioned chute.
All the rest of the unique weapons such as Ol' Painless, the Victory Rifle, and The Break can all be found by killing the person who has the desired weapon, lock picking or hacking into the container that holds the item, or by simply exploring the Wasteland.