Barrage: Astro's weapon is described as working only for those who have the qualifications. Initially, it's assumed to be his bravery and pure-heartedness, but it turns out that it's actually royal blood, which Astro secretly possesses.
Lightsabers in Star Wars can be effectively wielded only by Force-users, with very few exceptions. This is explained by the weapon's very counter-intuitive balance and preternatural quickness needed to wield it. Only one such exception is in the film canon, General Grievous, and he's a cyborg, with his mechanical precision of movements preventing him from julienning himself with the energy blades. The other film canon non-Force user who tries to handle a lightsaber, Han Solo, is wise enough to only use it to cut open a dead tauntaun. Also noteworthy is that Han is apparently well aware of how easily he could wind up missing chunks of himself, and keeps the hilt close to himself and his elbows tight to avoid swinging the blade around too much and winding up having to change his name to Han Duo.
In District 9 only prawns can use the prawn superweapons. Thus human Wikus becomes of interest to the authorities when he is infected with alien prawn DNA.
In Lone Wolf, only a Kai warrior such as Lone Wolf can wield the Sommerswerd. If anyone else tries to wield it, its powers would slowly fade until they were lost forever. The sword will also burn any evil beings who lay hands on it.
The Star Wars Expanded Universe novel The Crystal Star features a Jedi and Dark Jedi who have lightsabers that lack a traditional on/off switch. Instead, igniting them requires using the Force to close an internal electrical connection. In the New Jedi Order series the Skywalkers have a similar security feature on the bridge airlock of the Jade Shadow: opening the hatch from outside requires use of the Force to manipulate the internal mechanisms; the actual hand-operated latch is nonfunctional.
Lloyd Alexander's Chronicles of Prydain: Only a member of the House of Llyr, such as Princess Eilonwy, can command the power of her "bauble" (a.k.a. the Golden Pelydryn) and use the House's magical spells.
The Spear of Telesto in the Blood Angels novels can only be wielded by carriers of their Primarch Sanguinius' genes (i.e. just the Blood Angels and their successor chapters). Its flamethrower attack will likewise refuse to damage such.
Downplayed with wands, which have a certain loyalty to their owners and will not generally operate at full capacity for anyone else. Lore around the Elder Wand, a legendarily powerful item in Deathly Hallows, suggested that it may only work at full capacity for the person who has defeated (not necessarily killed) its last owner. Despite taking the wand from Dumbledore, it is no more powerful for Voldemort than his usual wand (which isn't saying much given the scale of Voldemort's powers), because he misread the chain of succession.Explanation (MAJOR SPOILER WARNING!) It was actually Draco Malfoy who defeated Dumbledore in Half-Blood Prince, and Harry defeated Draco in Deathly Hallows which caused the Elder Wand to pass to him.
Invoked by Dumbledore in Philosopher's Stone. He sets up the Mirror of Erised so that only somebody who wanted to get the Stone but not use it would be able to retrieve it.
Some Ancient technology (most famously the Puddle Jumpers) requires a genetic marker (quickly dubbed the Ancient Technology Activation [ATA] gene) to activate. This renders it inaccessible to most humans in the galaxy since the gene is recessive and tends to get bred out of smaller populations. Earth's is big enough to maintain it, and the SGC eventually developed a gene therapy to add the gene to their personnel.
Much Goa'uld technology requires bloodborne naquadah to activate, including the hand device and healing device. The most common way to get this is by hosting a Goa'uld, hence why Samantha Carter, who briefly carried a Tok'ra in "In the Line of Duty," can use them.
In season 2 an evil witch is released from a magical sleep and goes out seeking her wand. If she were to obtain it she would be nigh impossible to vanquish. The only way to destroy her would be to use her wand against her, but the only person capable of wielding it would be someone who was the seventh son of a seventh son.
In Season 8 Hippolyta's Belt would only let a morally good woman wear it or else it exploded.
In the Doctor Who episode "Dinosaurs on a Spaceship", the controls of the alien spaceship only respond to two pilots who are genetically linked. (How lucky that Rory's dad got dragged along on this adventure...)
In Fringeworthy, only a tiny percentage of the human race has the innate ability to use the Fringepaths without dying.
In Warhammer 40,000, Tau vehicles apparently use a genescanning system to prevent hijacking, as seen when an Imperial commando tried to steal a battlesuit and got fried for it.
Spell scrolls can usually only be activated by characters who can also access the spell through their class spell list (e.g. only a wizard or sorcerer can use a scroll of magic missile, only a cleric or druid can use one of flame strike, et cetera). This restriction can be overcome with a Use Magic Device check. Use Magic Device also lets you overcome several other restrictions, most of which fall under Level-Locked Loot.
Downplayed example: The Holy Avenger longsword is ordinarily "just" a +2 cold iron longsword. In the hands of a paladin it becomes a +5 holy cold iron longsword that also provides spell resistance to the wielder and anyone adjacent to them, as well as allowing them to cast greater dispel magic once per turn.
Sanctified and corrupt spells (from the 3E supplements Book of Exalted Deeds and Book of Vile Darkness, respectively) require the caster to be of a class that prepares spells and be of respectively good or evil Character Alignment.
NEXTs in Armored Core, which can only be piloted by people with some special type of psyche. Ill-defined, but still an example.
In The Elder Scrolls III: Morrowind, you must be wearing Wraithguard in order to handle Keening and Sunder without dying instantly. And in order to even wear Wraithguard, you must sacrifice a large portion of your health, permanently. If acquired the "standard" way, through Vivec, he will take you "outside of time and space" so that it doesn't harm you.
The player can't wear the Amulet of Kings; the clasp refuses to close. An in-game book, The Amulet of Kings, explains that it can only be worn by those who have "Dragon Blood" in their veins. This was initially unclear in meaning, but with the release of Skyrim it's evident that it refers to the Dovahkiin (Dragonborn), humanoids with the souls of dragons, of whom the Septim Dynasty is one line.
The Divine Crusader equipment set in Knights of the Nine. To use it, you need to go on a long, annoying pilgrimage, and if your Infamy is raised to anything above 1 after you have obtained it, then you must go on said pilgrimage again.
The Apple of Eden in Assassin's Creed can only be used by descendants of the first civilization.
Various items in the Neverwinter Nights series are keyed to a particular race, class, and/or alignment. For example, the sequel's Hammer of Ironfist can only be wielded by dwarves, and many prestige classes have unique armors. A successful Use Magic Device check will override these restrictions, however.
In the Paper Mario: The Thousand-Year Door intro, the chest containing the magical map that the merchant gives Peach says that only someone pure of heart can open it. Peach was able to open it. Later, it is revealed that The merchant was actually Beldam in disguise; who did so because she was trying to unseal the Shadow Queen, and needed the Crystal Stars to do so since the Crystal Stars are needed to open the Thousand Year Door, which is where the Shadow Queen is sealed. The magical map is what allows you to find them.
In Tales From My D&D Campaign, the evil Kua-Toa have found out how to power an alchemical Invisibilty Cloak using their skin secretions. This not only lets them produce the cloaks for 1/100th of what such a powerful item should cost, but also makes them impossible to steal, as only a living Kua Toa can produce the chemicals that power the thing.
Regular Show has the Sandwich of Death, which is deadly unless you eat it the right way: by wearing a mullet and cut-off shorts.