Regeneration

Summary
Regeneration, often referred to as a healing factor, is the ability to heal from wounds at an accelerated rate, with many characters proving capable of regenerating from wounds that would be lethal to normal humans.

It has several different levels that range in potency from what is essentially just faster natural healing to being able to regrow limbs or organs, or even a severed head.

Higher levels allow characters to regenerate from even more severe wounds, such as being blown to pieces, reduced to a single cell, vaporization, and even complete physical destruction and beyond.

Instances of characters being wounded and inexplicably recovering off screen should not be taken as evidence of regeneration unless supported by further context. This is due to reasons ranging from possibility of off-screen treatment to continuity errors. See this thread for reference.

Types
Low: Merely an accelerated healing ability for normal wounds, allowing the character to heal wounds that would normally take days, weeks, or even months much more quickly, sometimes even in just seconds. For machines and vehicles, this would just be regenerating basic exterior damage.
 * Examples: Naruto (Naruto)

Mid-Low: The ability to heal wounds that would normally leave large scars, such as severe burns or deep injuries. For machines and vehicles, this would be regenerating damage that would normally leave large dents and openings.
 * Examples: Link (The Legend of Zelda), Blade (Marvel Comics), Yusuke Urameshi (Yu Yu Hakusho)

High-Low: The ability to regenerate severed fingers, toes, or ears, minor organ damage, and even potentially reattach lost limbs. For machines and vehicles, this would be regenerating some interior damage, along with some minor critically damaged or destroyed parts.
 * Examples: Toa (Bionicle), Wally West (DC Comics), Hercules (Marvel Comics)

Low-Mid: The ability to regenerate lost limbs, and even from severe organ damage or destruction, including traditionally fatal wounds and disembowelment or horizontal bisection. For machines and vehicles, this would be regenerating minor parts and more extensive internal damage.
 * Examples: Piccolo and other Namekians (Dragon Ball), Shirou Emiya / Saber with Avalon (Fate/stay night)

Mid: The ability to regenerate from decapitation or severe brain damage. For machines and vehicles, this would be regenerating from the destruction of critical parts, such as the engine.
 * Examples: Dante (Devil May Cry), Sayaka Miki (Puella Magi Madoka Magica)

High-Mid: The ability to regenerate from being blown / cut to pieces, or from a small piece of the user's body, such as a severed head, a single organ, or a finger.
 * Examples: Meta-Cooler (Dragon Ball), Dio Brando (JoJo's Bizarre Adventure), Ryūko Matoi (Kill la Kill)

Low-High: The ability to regenerate from having no solid parts of the body remaining. This can range from a puddle or drop of blood to even a single cell. For robots and machines, this can also include regenerating from a liquid state.
 * Examples: Cell (Dragon Ball), Homunculi (Fullmetal Alchemist), Alucard (Hellsing), Wolverine (Marvel Comics)

Mid-High: The ability to regenerate from having all biology completely incinerated. This includes being reduced to ash, dust, smoke, vapor, or plasma.
 * Examples: Majin Buu (Dragon Ball), Dark Matter (Kirby), Deadpool and Hulk (Marvel Comics), Ban (Nanatsu no Taizai), Logia Devil Fruit users such as Portgas D. Ace (One Piece)

High: The ability to regenerate from a few scattered or lone molecules, atoms, or sub-atomic particles.
 * Examples: The Sentry (Marvel Comics), Kakine Teitoku (To Aru Majutsu No Index)

Low-Godly: The ability to regenerate from the complete physical destruction of the user's body, instead restoring it from their disembodied consciousness, whether that be their soul, mind, some other nonphysical aspect of themself, esoteric or metaphysical energy, or something else.
 * Examples: Dark Schneider (Bastard!!), Sosuke Aizen (Bleach), UlforceVeedramon (Digimon), Spawn (Image Comics), Hourai Immortals (Touhou Project)

Mid-Godly: The ability to regenerate from the complete erasure of body, mind, and soul.
 * Examples: Gods from Saint Seiya, Indramon (Digimon)

High-Godly: The ability to regenerate after the erasure of body, mind, and soul, along with at least one even more fundamental aspect of a character's existence, such as their place in the narrative, their entire history, or the underlying concept(s) or information needed for them to exist.
 * Examples: Demons from Shin Megami Tensei, Kriemhild Gretchen (Puella Magi Madoka Magica), Yggdrasil (Digimon), Lavos (Chrono), Sailor Moon

Beyond-Godly: The ability to regenerate from nothing at all. Characters with this type of regeneration have to be far superior and transcend characters with High-Godly regeneration. This type of regeneration is reserved for 1-B chracters and above. Characters with this type of regeneration can only be exterminated by characters with the ability of conceptional denial on higher planes of existence.
 * Examples: Gods as Gerold Haynaly