Great Big Library of Everything-Quite a few of these, actually. Assuming you don’t count the Wired itself as a huge storage repository, you have the Canterlot Main Library, which is the single largest building on Equestria, let alone library. The main library wing is so large, it has a dedicated pegasus weather team to keep the humidity down to prevent damage to the books. The card catalogue was printed once, and it came out to something around twenty million pages of 8 1/2×11″ paper. The specialist library sections are built to scale. Pretty much everything that has ever been produced or published or otherwise created within the Kingdom has a copy stored at the Canterlot Main Library, or one of the storage branches scattered throughout Equestria or the Kingdom proper.
Runner up for this is the House of Knowledge in the Zebra Imperium. The Griffin Moot boasts that the Library Of Wonders is larger, but it doesn’t have the same history and gravitas as the Canterlot Main Library.
For secret libraries, the Ministry of Ghosts maintains the Silent Library-a repository of dangerous magic, artifacts, and things that should never be let out…somewhere. The Special Working Group has the Ghost Floats, a number of ships that store dangerous things on perpetual looping missions through the entire Griffin Moot. Unit 999 has a storage archive…somewhere, as well as the Silent Ones.