The Xenomorph king is a special type of Alien rarely seen in the Alien lore. It is known to be bigger than the queen Alien and even more aggressive. There is no evidence of the Xenomorph king ever mating with a Xenomorph queen. They are more likely to fight. Here is a list of all notable Xenomorph kings from the Aliens lore, including comics and action figures.
The Rogue Xenomorph was a genetic experiment created by Professor Ernst Kleist at Charon Base, a remote outpost embedded in an asteroid. It was a creature bigger than all the other known Alien types at the time, including the queen. It had purplish skin, spikes all over its body, and a huge head. The aim of this twisted experiment was to create a control mechanism for Xenomorphs outside of the influence of the Queen. The Rogue was only featured in the Aliens: Rogue comic book and novel, with the book being much better than the graphic novel.
Xenomorph King vs. Xenomorph Queen
Although the Rogue Xenomorph felt no loyalty towards the hive or the Queen, it did feel a sudden urge to meet her, motivating the King to escape from his prison. This urge was not an attempt to mate with the Queen, but rather a curiosity to meet her at first. As the Rogue rampaged through Charon Base, it killed both human soldiers and regular Xenomorphs, letting nothing stand in its way. When it finally met the Queen, they stared down at each other and started a vicious fight. Although it seemed that the King had an advantage in size and strength, the Queen was smarter and wore the King down with her agility. The Queen managed to fatally wound the King, but the victor did not really matter as the base was obliterated by an unstable Sound Cannon exploding.
The Hybrid King
Not a Xenomorph king per se, the hybrid king was the leader of the genetically-engineered hybrid creatures created by the corrupted AI computer mainframe "TOY". The hybrids possessed traits of Xenomorphs, Yautja, and humans. Physically, it was perhaps most similar to a Predalien but with white skin. The Hybrid king was bigger and stronger than the regular white hybrids or Xenomorphs. It had a high level of intelligence and could even speak. Similarly to the Rogue, it had spikes on its body and is killed by a queen Alien. The hybrid king was featured in the Aliens vs. Predator: Deadliest of the Species comic book, which is part of Aliens vs. Predator Omnibus: Volume 2.
The Kenner King Alien
In 1994, Kenner released the 4th series of Aliens action figures. It included the King Alien. The King Alien came with a 2-pack along with a Dwayne Hicks figure. It was also released separately, but with a greenish paint job. Although previous Kenner action figures came with a small comic book, the King Alien figures were missing this feature. The other action figure comics did not feature it either, so there is not much explanation for its existence (other than to sell awesome toys). It is hoped that NECA will make a figure based on this Xenomorph king, as they have done so in the past with other figures.
The Sideshow Alien King
In 2016, the Sideshow Collectibles released an Alien King Maquette to celebrate the 30th anniversary of Aliens. Partly inspired by Giger's original designs, and partly by the Rogue Alien, it is quite an awesome figure. Compared to regular Xenomorphs standing on its base, the Xenomorph king is about 5 times bigger than them. Its head crest is perhaps slightly smaller than the queens, but its legs are more muscular, and the dorsal tubes are longer. It has a brownish tint, similar to the Xenos from Alien: Resurrection.
The King-Sized Alien from Aliens: Armageddon
In an unusual way to introduce a big boss-type enemy, the Aliens: Armageddon arcade game threw a King-size enemy at the play in the first five minutes of the game. This giant shoved aside regular Xenomorphs and attacked the player with his claws and tail. The player could shoot at his weak spots, making him retreat for a while. This brown-skinned Alien King appeared a few more times, until another surprising twist. A flying Xenomorph Queen emerged from the sky, ambushed the Xenomorph King, and ripped him apart. This happened in the middle of this relatively short game (about 30 minutes in total) and the Flying Queen became the next boss enemy. This is similar to what happened in Aliens: Rogue, although the King put up a stronger fight against the Alien Queen there.