In the Alpha build of the game and its E3 2015 demo, it would have originally revealed story elements in the form of "Epitaphs", small gravestones spread throughout Lothric which upon offering a flame to it will display a text blurb with a lore-related message on each. In the English version of the Alpha build, some Epitaphs have no text due to the feature having been scrapped by that time, however in the Japanese version of the Alpha build, the data for all Epitaph texts and most of their physical placements on the game's map exist, albeit some are out of bounds or clustered together as their locations had not been finalized before being scrapped.
Contributed by MehDeletingLater
Filianore from the Ringed City DLC is a reference to the film Angel's Egg.
Contributed by DrakeVagabond
There are cut animations to an unused game mechanic that would have allowed players to create their own Bonfires. It was even present in a trailer shown at Gamescom 2015, showing a knight placing a Bonfire sword into a body and igniting it.
The first animation set found in the game's files shows the aforementioned placing of the sword, along with one removing the sword from a body. The second set shows an animation using both hands to insert the sword, then an idle "prayer" animation. In one of the leaked screenshots, this animation is seen with a black fire rising from a body, possibly being absorbed by the player.
It was likely cut due to gameplay balance issues, as it would effectively remove the need to travel an intended path to a specific goal, ie a boss fog gate. It would have also likely created issues with enemies that respawn after sitting at a bonfire.
Contributed by G-Haven
If the player uses a gesture while in front of the Fire Keeper at Firelink Shrine, she will react to it by either bowing, twirling around, laughing, or turning her head away. The "Path of the Dragon" gesture in particular makes her twirl around continuously until the player gets back up.

This is a carryover from the previous "Souls" game Bloodborne, where the supporting character responsible for helping the player level-up reacts to the player's gestures performed in front of them.
Contributed by G-Haven
An optional glitched route can be used early in the game to access the the top of Firelink Shrine for free. By running towards a tree situated next to the roof and performing an extremely well-timed jump, the player can make it onto the top of the shrine without having to spend 20,000 souls on the tower key, which is normally required to access the area. Doing this will also net the player an extra Estus Flask, which can found in the upper rafters of Firelink Shrine.
Contributed by Thehydraofficial
NSFW - This trivia is considered "Not Safe for Work" - Click to Reveal
In the fight with Spoiler:Oceiros the Consumed King, Oceiros goes through the first half of the fight holding what appears to be nothing in his hand, giving the impression that a baby named "Ocelotte" is either invisible or simply does not exist and is just a delusion in Oceiros's mind.

However, there are several files still in the game data (including model, model-skeleton, textures and sound files) that show at one point, there was indeed a baby held in his hand. The most likely reason the baby was removed in the final game is because it would have been considered "too graphic" for various game-rating boards, as the baby is killed mid-fight in a very explicit manner.
Contributed by G-Haven
Like the Doll from Bloodborne, the Firekeeper will react to emotes. In particular, the "Toast" emote acquired from Siegward will make the Firekeeper twirl. This is the only emote that causes this reaction.
Contributed by DrakeVagabond