Similar to the possible races, official classes, and 4e backgrounds questions, what are official WotC-published backgrounds available for players, and which books/resources contain them?
By official, I mean that the backgrounds are available for Adventurers League Play. While other backgrounds from Unearthed Arcana or from other WotC sources outside the D&D team are of interest, please mention whether they're considered official and sanctioned or not.
The Adventurers League Player's Guide covers what is a legal DDAL resource. From the AL Player's Guide v11.0:
You can use non-optional rules found in the Player’s Handbook, the Basic Rules, and all the books listed below.
Also worth noting is that D&D Adventurer's League supports customizing a background, as per the PHB rules for doing so. While this allows for a custom selection of skill proficiency and tool/language proficiency, you're still restricted to equipment packages and background features as published.
In addition, Baldur's Gate: Descent into Avernus contains alternate features for all 13 of the PHB backgrounds.
MOONSHAE ISLES & BORDER KINGDOM CHARACTERS
If you’re participating in adventures set in either of these locations, you can use their respective products (found on the DMs Guild) to select a background for your character. Rising Shadows-Moonshae Isles Regional Guide
The Border Kingdoms: A Forgotten Realms Campaign Supplement
The information for older editions can be found here:
