Artifact Collection Agency

An Artifact Collection Agency is a group of people who make it their business to collect mysterious artifacts. Sometimes this is done to protect the artifacts from misuse, or to protect the world from the artifacts which are considered inherently dangerous. Of course, collectors can have ulterior motives, too.

Though they are more often run by the government, sometimes private citizens form Artifact Collection Agencies and create fabulous repositories for them in the form of the Bazaar of the Bizarre, Trophy Room or Superhero Trophy Shelf. Governmental artifact collectors will often have a Secret Government Warehouse where recovered artifacts are kept under lock and key.

Common artifacts they collect can include: Artifact of Death, Artifact of Doom, Artifact of Attraction, Clingy MacGuffin, MacGuffin, Empathic Weapon, Amplifier Artifact, Tome of Eldritch Lore.

Of course, they Gotta Catch Them All.

Examples of Artifact Collection Agency include:

Anime and Manga

The Speedwagon Foundation in JoJo's Bizarre Adventure works in conjunction with the Joestar family to collect and research the various supernatural MacGuffins throughout the series, such as the vampire-creating Stone Masks and the Psychic Powers-bestowing Stand Arrows.
One of the primary objectives of the Time-Space Administration Bureau in Magical Girl Lyrical Nanoha franchise has always been securing the Lost Logia, magical artifacts created for the centuries-long Saint King Unification War (or even earlier Belkan wars). The reason for this is that Lost Logia are extremely dangerous to unsuspecting civilians and even more so in criminal hands, although some minds within TSAB have also tried to weaponize Lost Logia themselves.
The Society from Dragon Crisis collects artifacts called "Lost Preciouses". The more powerful/dangerous ones are usually locked away in vaults, while individual members of the Society have their own private collections. Eriko also started up her own Lost Precious collection agency called Seven Tails that specializes in acquiring and recovering Lost Preciouses.

Film

The Secret Government Warehouse seen at the end of Raiders of the Lost Ark implies the existence of such an agency: It's far too large to only contain things stumbled upon by chance.
- Unless it's just an ordinary warehouse and they dumped the Ark in there for lack of a better idea of what to do it.
As mentioned below in the Live Action TV section, this happens in Stargate. It is worth mentioning that Stargate Command (the operation which runs the Stargate on the tv show) doesn't exist yet during the movie, so in this case the artifact collecting agency is the US Air Force.

Literature

The Doctor Who New Adventures novels have the Library of St John the Beheaded, which collects and preserves books and manuscripts containing information for which The World Is Not Ready.
In the Bernice Summerfield series the Braxiatel Collection is this.
In The Wheel of Time, the White Tower claims all sa'angreal, angreal, and ter'angreal for itself, arguing that they are too dangerous to be handled by anyone else (sometimes this is true). The government of Tear also tries to accumulate as many ancient artifacts as possible, with the argument that they need to keep them all out of the hands of the Tower and the Dragon.

Live Action TV

Friday the 13th: The Series.
Warehouse 13, in which the secret branch of the Secret Service is tasked with collecting them.
- Actually, the Warehouse (and its 12 predecessors) is run by an Ancient Tradition dating back to Ancient Egypt, and its field agents are recruited from any government agency (or sometimes, civilians) if/when deemed worthy of the position. The fact that the current agents are both Secret Service is coincidence.
  - This troper got the impression that agents from the country where the current warehouse was located got first pass in recruiting. For example, in the alternate universe where Pete never existed both of the Warehouse agents are still secret service, all the agents known to have worked at Warehouse 12 were British and almost all past Warehouse 13 operatives were American.
The Lost Room, which actually had several such groups.
In the Stargate franchise, this is part of Stargate Command's charter. Basically, their mission is "Go find alien tech we can use to defend the Earth against hostile ETs."
- Also in the Stargate franchise, the NID takes on the same function but with a more aggressive, less scrupulous and eventually illegal approach. Its successor, The Trust, is even worse.
This is an important part of Torchwood's charter, in both Torchwood and Doctor Who. Unofficial motto: "If It's Alien, It's Ours." They have a nasty tendency to forget their other priorities (like the bit about defending the realm), in fact.
In the Librarian trilogy of TV movies, the Metropolitan Library is an Artifact Collection Agency.
Go Go Sentai Boukenger has two collection agencies: The Negative Syndicate [the bad guys], and the Search Guard Successor Foundation.

Tabletop Games

In Shadowrun, the Mystic Crusaders organization acquires ancient magic items and artifacts for the Atlantean Foundation.
Hunter: The Vigil has the Aegis Kai Doru, who collect artifacts to use against supernaturals.
The GURPS Warehouse 23 setting.

Video Games

Exile 3‍'‍s Cult of the Sacred Item.
Merchants in every role playing game ever. Whether they sell them to the player or buy the goods, these people see many of the most dangerous artifacts in existence.
The Moebius Foundation in the Starcraft II: Wings of Liberty single player campaign. Their mission is to collect a set of Xel'Naga artifacts, and they hire Raynor's Raiders to do the legwork. However, the Moebius Foundation is really a front organization set up by the emperor's son, Valerian Mengsk.

Web Comics

The defunct web comic The Repository of Dangerous Things.
RCSI in Code Name: Hunter is described as having this as one of its duties
- Although to be fair we hardly see any sort of artifact except for a cursed drum set and a smoking wooden box
Girl Genius got Corbettite monks with their vaults. When things get there, it's not because people just ask monks to hold onto something simple and safe for a while.

Father Gerät: Some were used against us and confiscated. Some were simply found, with no one to ask of their purpose. In some cases, no one for kilometers around, the records say.

- It turns out occasionally they let some Mad Scientist from outside (the problem is finding one both competent and trustworthy) help with study and neutralization. And that the Incorruptible Library grew from collection of notes on such exercises (and presumably references used).

Web Original

The SCP Foundation is a worldwide organization supported by multiple governments. It collects artifacts to study them, to protect humans from the artifacts, and to protect normalcy, meaning that they keep secret the existence of even the most harmless of artifacts in order to keep the world ignorant of the existence of the paranormal.
The Basement of Warehouse 23, Steve Jackson Games' online store.