Record of Lodoss War took this to an extreme, with a set of magical halberds enchanted to slay one specific dragon. These were effective despite the heroes having to jump off a cliff to hit the dragon's head.
One story arc in A Certain Magical Index revolves around a weapon called the Stab Sword, which is able to kill immensely powerful magic users.
Technically the Zanpakuto swords from Bleach are used to release dead souls and cut down Hollows. This doesn't make them any better or worse at actually fighting Hollows specifically.
Digimon Adventure: Wargreymon's spiked gauntlets are called "Dramon Destroyers"; they give him a particular advantage against MetalSeadramon and Machinedramon.
The Dragonslayer from Berserk didn't start out as one of thesenote While it has its name from a king commissioning a weapon capable of killing a dragon, its forger had never seen a dragon or even known if they existed, so nothing makes it specialized in actual dragon slaying., but after years of Guts using it against demons, it eventually gains the ability to kill even demons that are ethereal are impervious to normal weapons. It is speculated that it can even wound the Godhand themselves.
Inverted in Munchkin by the "sword of slaying everything except squid". It gives a substantial bonus but against squid (there are two in the decks so far — karate squid and Squidzilla) the fight is automatically lost.
The Sommerswerd, devastating against undead, and deadly even for the Darklords. It is stated later it could be lethal even against Naar. To be honest, it's quite good at killing anything anyway.
The various evil weapons favored by the Darklords have one thing in common: they give combat bonus against other Darklords, and are among the very few things able to kill them permanently. Those guys truly had their priorities in order.
The jewelled mace from book 5 gives a bonus against illusory creatures.
The enchanted bullwhip from book 10 can hit (and gives a bonus against) specters.
The Dessi Stone is a magic gem that, when merged into the hilt of any ordinary weapon, can turn it into an undead slayer.
Several of the weapons forged by Lone Wolf with Kai Weaponcraft in the New Order series have a CS bonus when used against specific creatures, like reptiles, undead, stone beings, magic-users, flying monsters or fire-breathers, respectively.
The eponymous weapons of the Dragonlance setting are exceptionally effective against dragons.
In Lord Demon, many of the demons have weapons that are attuned to kill them specifically. Kai Wren shows up to one duel wielding the sword made to kill his opponent, and the wounds he sustains don't heal properly. Kai Wren also has an Oh Crap moment when he realizes just who has the weapon made to kill him.
The first is the energy weapon for killing Anubis'Kull warriors, which is of indeterminate use against anything else but will kill Kull in a couple shots by negating the Ancient phlebotinum that brought them to life in the first place.
The second is the Replicator disruptor and the anti-Replicator gun later adapted from it, weapons built using Ancient knowledge that disrupts the ability of individual Replicator blocks to communicate with each other.
Finally, the weapon Merlin designed to destroy ascended beings, which is finally used to wipe out the Ori in season 10.
Final Fantasy IX allows characters to equip various "killer" abilities (e.g. Demonkiller, Birdkiller) that cause whatever weapon they have to deal bonus damage.
Angband has a set of Slay X properties (Evil, Orc, Demon, Undead, Troll, Giant, Animal, and Dragon), which can be found in various combinations on ego and artifact weapons.
ADOM followed a similar model to Angband; the possible values of X in this case included humanoids (which category included some bosses and most elite mooks).
Dungeon Crawl has weapons of orc slaying, which simply give a damage bonus against orcs.
Several of the artifact weapons in NetHack fall into this category e.g. Ogresmasher, Werebane (which happens to also invoke Depleted Phlebotinum Shells, since it's a silver saber), and Orcrist. Additionally Vorpal Blade, which can One-Hit Kill anything with a head 5% of the time, does so 100% of the time against jabberwocks.
Diablo gives all blunt weapons this effect against undead monsters.
Diablo II also has weapons with specific anti-undead or anti-demon enchantments.
Diablo III has weapons and other equipment that give damage bonuses against elite monsters, which are particularly prized in high-level play.
Weapons with bonuses against the Darkspawn, undead, and/or demons are pretty commonplace in the Dragon Age series, but Dragon Age II also has a greatsword with a large bonus against Qunari. Fittingly, you pick it up shortly before storming a Qunari stronghold. In the following act, a Qunari gives you a sword specialized against humans (probably as a stealth comeback).
The series has a whole range of Slayer weapons — they tend to be breakable, making them Too Awesome to Use against anything but bosses. The game only rolls to see if a weapon breaks at the start of your enemy's turn, however, so if you finish the battle in one round, it will never make the check, allowing them to last you through the whole game. As the weapons are uniformly a one-hit kill, the only real danger of losing them comes when you're facing more than one such enemy, which happens rarely, and only after you've had the opportunity to pick up multiple weapons of the type.
In addition to the Slayer weapons, there are also weapons that have a Death effect based on a given element. With these, the weapon will instantly kill anything that has that elemental weakness, regardless of total HP or defenses. This includes the penultimate boss on the way to the Golden Ending, who can be killed in one round by a sword you picked up around the midpoint of the game.
RuneScape has several examples, including Silverlight (and its upgraded form, Darklight) for slaying demons; Balmung, the Battleaxe of Dagannoth Slaying; the Ivandis Flail, used for killing Vyrewatch vampyres; and the brackish blade and brine sabre, which are super-effective against crabs for some reason.
Shining Force has a variety of specialized weapons that are strong against specific types of enemies — the Mermanbuster is strong against sea creatures, the Jagged Flash is strong against flying enemies, the Elf Slayer is good against robots, and so on.
The Legend of Dragoon has two ancient weapons forged to defeat Dragons and Dragoons: one of them was the Dragon Buster sword, capable of piercing the Dragoon armor. Unlike most video game examples, it's your enemy that wields it, handicapping you during your battles against him.
EverQuest has a "Bane" effect which increases damage towards a particular species of monsters.
Wizardry has weapons dealing double damage to specific types. 7-th has weapons against Dragon, Robot, Undead and, due to a silly bug, Fighter; in 8-th against Android, Beast, Demon, Dragon, Plant and Undead.
Crossfire adventure game has slaying weapons, and when a deity blesses someone's weapon, it usually acquires the slaying property vs. the kind of creatures this deity doesn't like.
Most games in the Dragon Quest franchise have an assortment of these, doing higher damage against the designated enemy (e.g. weapons with "metal" at the start of the name usually do extra damage when they hit a Metal Slime, while the dragonsbane does extra damage to dragons).
In Drakensang, dwarves have the Wyrmslayer Ax (a small hatchet with a very big blade) and also the Dragonslayer Axe, the Dragon-Crushing hammer, the Dragon-Piercer crossbow and the Dragon Spear (as in a trident made for skewering dragons). Yes, before you ask, dwarves hate dragons, and even have something like seven different words to define the death of a dragon.
Kingdom Hearts: Chain of Memories played this straight and averted it, by giving various cards elements, using fire type against water-type gives an extra attack boost. However using the same element heals them.
Fall Out 3 has pulse grenades and pulse mines dedicated to fighting robots. There is also a stick that makes mole rats heads explode.
There's a woodcutting axe that does extra damage to animals (which can then be disenchanted and applied to other weapons); and the artifact axe Wuuthrad does more damage to Elves.
There also exists a weapon that does more damage to Nords in the game's code, but it's sadly Dummied Out.
The Daedric artefact Dawnbreaker, which not only sets regular foes on fire but does extra damage to undead, the latter of which can trigger an explosive shockwave that either delivers a One-Hit Kill to any remaining undead or makes them run for the hills.
Dragonbane, a one-handed sword you obtain in Sky Haven Temple, does extra damage against dragons and shock damage against everything else. It's impractical against the latter though, since its charge is low and unlike other shock weapons it doesn't drain magicka.
Dawnguard give us a series of weapons than do extra damage against vampires and the bow of a god that does extra damage against undead.
Minecraft has two sword enchantments in this category: "Smite" gives a damage bonus against undead enemies, while "Bane of Arthropods" gives this bonus against spiders and silverfish.
Lufia II: Rise of the Sinistrals has a set of weapons that are extra effective against giant spiders, another that is the same for lizard (including dragons). Another set, much later, effects only dragons but has a higher base damage than the anti-lizard set.
Earthbound has spray bottles filled with Rust Promoter (which damages robots) and Insecticide (guess).
A quest in The Sims Medieval requires you to make a dragon-slaying sword called Wyrmslayer.
Roommates makes the Orcrist this against Goblins, and even more against anybody currently holding the Goblin King title.
The Finger of Hell, a knife custom-designed by Dellyn (a Fantastic RacistTorture Technician) to inflict excruciating pain if used against a goblin; it's implied each of his tools has been custom-made to be particularly effective if used to torture members of a particular race.
Minmax finds a 'Racist Axe' that gains an accuracy and damage bonus if the wielder is the same race as their target. He gives it to his comrade Forgath when they're attacked by Kore, since both Kore and Forgath are dwarves.
In The Order of the Stick, when Roy's Ancestral Greatsword is reforged with starmetal, one of the properties it gains is to sometimes emit a deadly green energy which is particularly harmful to the undead. The blacksmith offers to supress this power, but Roy declines, since his quest involves the destruction of a particularly powerful lich.