Successful

Villains who win against the hero (or other rival villains) and/or are successful in their ultimate goals. Some examples include:

• Alejandro Sosa getting Tony Montana and his henchmen killed for failing the assassination attempt on an anti-Bolivian activist in Scarface.
• Audrey II taking over the world with its children in the original ending of Little Shop of Horrors.
• Shadow the Hedgehog destroying, enslaving or saving the world based on the player's choices in Shadow the Hedgehog.
• Thanos collecting the Infinity Stones to wipe out half of the universe's populace in Avengers: Infinity War.

They are, usually, the opposite of Incompetent villains (who do not succeed in anything), though some Incompetent villains can still be successful either with a huge stroke of luck, with the help of much more competent evildoers, or by learning from their own mistakes to become better.

It should be noted that for some villains, their goal was not to kill the main protagonist. Notably, successful villains are very common in many modern-day horror movies (e.g. Freddy Krueger, Jason Voorhees, Godzilla, Kayako Saeki, etc.) as well as some tragic fictional works (e.g. Padre Dámasore, Iago, etc.) in which many of these villains succeeded in killing the protagonist in the end.

In many works, a successful villain can be a Protagonist since protagonists are known for winning in the end.

Though these two categories often overlap, this is not to be confused with Karma Houdinis, as these villains, despite their success, can still be defeated later, usually at the end of the story if their success occurred at the beginning or middle of it, or in a sequel since some villain victories open the doors for sequels (e.g. Archibald Snatcher succeeded to get his White Hat and taste cheese, but his allergy caused him to explode or Scar finally becoming the King of the Pride Lands after killing his brother and banishing his nephew, only to be dethroned by said nephew and killed by his hyena henchman at the end of the movie) and conversely, they cannot be ever defeated despite their failure. However, some villains that are successful can also be Karma Houdinis if they are successful enough, such as Rustal Elion.

Also, sometimes these villains finally succeed in their goals, but not in the way they expected (e.g. Wile E. Coyote finally catching the Road Runner, but only when he became too small to eat him; Chef Skinner getting Gusteau's closed for rat infestation but Linguini and Remy are still able to open the Ratatouille, Tai Lung obtaining the Dragon Scroll but failing to realize the significance behind it and Max Mordon obtaining immortality, but in the form of an undead mummy) or they didn't get to enjoy it (e.g. Marty Wolf turned Big Fat Liar into a critical and financial hit but lost his job and fame for plagiarizing Jason Shepherd's work, Brad Gurdlinger got Pablo Chacon arrested and removed from the drug business but was taken into custody as well).