Hammer

The Hammer is an anomalous power-up in Super Mario 64, obviously being based off of the hammer used throughout the Super Mario Bros. series, such as the hammer in Donkey Kong or the Hammer Suit in Super Mario Bros. 3, both of which have notably been reported to appear in the game. This anomaly is fittingly rare, as it is likely hard for the Personalization A.I. to re-integrate a power-up back into Super Mario 64. Which version of the anomaly is real is currently debated though.

Version 1
The most common version of the Hammer appearing in Super Mario 64 is the standard hammer item itself appearing. It usually appears on it's own without a Cap Switch level, simply appearing on the ground or in a yellow ! box. The Hammer can be used to hit enemies, break boxes, and can even hit unique switches, sometimes even underwater if the power-up allows the player to walk underwater or if it is used in combination with the Metal Cap. This has reportedly unlocked several anomalous areas, for example, requiring the player to hammer a switch to drain the Castle Grounds and reach the level that unlocks the Frog Cap.

Version 2
Also known as the Hammer Cap, this version of the Hammer power-up supposedly resembles the Super Mario Bros. 3 Hammer Suit much more than the other version, allowing the player to throw hammers instead of simply holding them to damage enemies, break objects and press switches, apparently the constant between both versions of the anomaly. This cap is most commonly acquired after defeating the anomalous Hammer Bros. boss fight, or clearing some kind of level that involves them, likely due to their association with hammers.

Unlocking
If the Hammer or Hammer Cap requires the player to unlock it via a Cap Switch level, it most commonly appears in a level nicknamed "Hammer Down Dam" by those who have encountered it. The level itself is commonly described as a large water reserve next to a dam. The water itself is typically murky and hard to see through, and reportedly damages the player faster than regular water. The main goal of this level is to go to the dam and use the Hammer to break through several blocks and broken walls to press switches to gradually lower the water level, allowing access to more parts of the dam, until the player reaches the bottom where the Cap Switch for the Hammer is typically found, commonly being a black Cap Switch. Similarly to all Cap Switch levels, this level also reportedly has a Power Star unlocked by collecting 8 red coins.