There are 2 currently confirmed endings to Breath of the Wild:
1) Basic Ending:
This is the easier of the two endings, and is achieved upon defeating Ganon's true form, without having completed all of the side-missions and extras throughout the game.
Zelda appears, and seals the evil away. Before the credits, Zelda asks Link if he truly remembers her. the credits then roll.
You can watch the Basic Ending here.
2) True Ending
This ending is unlocked by collecting all 18 of Link's memories.
It is caled the "True Ending" because the basic ending is an "incomplete" version of this ending. After the credits roll and shows Link and Zelda together again, in their Hylian garb, looking upon a Hyrule that’s full of life and devoid of any evil forces. Zelda’s work isn’t done though. She’s going to work to keep the peace and make sure that everyone’s prepared for the next time Ganon decides to show up. She’s rebuilding the kingdom and ensuring that nothing so horrible ever happens again. And she intends to do all of this without her powers which have gone dormant after Ganon was sealed. She smiles, content with her being without any extra abilities as she and Link set out to ride their horses to the Zora Domain to take care of Divine Beast Vah Ruta.
You can watch the True Ending here.