The first Predator film came out in 1987, and became fairly famous. The plot consisted of a team of US soldiers being hunted down and murdered one by one by some unknown and sinister creature. Various glimpses of the creature are seen throughout, but towards the end of the movie, the Predator finally reveals himself and his ugly mug to the protagonist in all his glory. The Predator wasn't really given any sort of nickname, until at one point he was given the identity of 'Jungle Hunter'.

Something of an ugly bugger when their mask is taken off, predators look quite imposing. Standing over 7' tall and covered in odd technology, they really are a sight in the movies.
The Jungle Hunter unmasked:

In the second movie, Predator 2, a new predator was to be the hunter, stalking violent men through city streets.

The so-called City Hunter is again eventually killed by the protagonist, revealing another three predators, or Elders.

Leaving about a decade, the Predators returned in a film crossover with the Aliens franchise: Aliens Vs Predator. This time, three predators are seen mass-murdering humans and aliens alike, although eventually killed one by one by the aliens. These are the nastiest-looking so far and were given nicknames: Celtic, Chopper and Scar, each having their own distinctive masks
Celtic, the leader and most brutal of the trio:

Chopper, having got his name by way of his wristblades being longer and meaner than those of the other two:

And Scar: the longest-lived and more famous of the three:

In the sequel to this film, Alien Vs Predator Requiem was released in 2007, featuring another Predator, Wolf, named on account of his sinister mask.

Wolf's mission is to contain the emergent Alien threat in the film and hunt down the abominations.

In the latest movie, Predators, a further four predators make themselves known. The first three are the nastiest as yet, being bigger, stronger and far more vicious than any of the others. The name given to them is 'Super Predators, on account of their being superior to other predators. The fourth predator in the film is another Jungle Hunter, similar to that in the first film. The super predators are also given nicknames: Falconer, Tracker, and the leader, Berserker.

Tracker is the first to meet his death at the hand of one of the film's humans. He makes extensive use of traps to hunt his prey

Falconer is the second of the three to be brought down by one of the humans. He makes use of a single, long wristblade and a mechanical scouting falcon to spot prey.

The Berserker, also affectionately named 'Mr Black' on account of his dark skin, is the most badass of the three, killing not only several of the humans, but the fourth predator in the film as well. He is the most ferocious killing machine of all predators seen yet, and my personal favourite, just ahead of Celtic and Dark.

The thing which sets apart Mr Black from the other predators is his face, which is the most utterly demonic of all of them.
While most unmasked predators , while still incredibly ugly, look something like this:

..Mr Black, without his mask, looks like this:

The fourth Predator in the film is somewhat smaller than the three super predators, reminiscent of Jungle Hunter in the first film. He is killed by the Berserker towards the end.

One other predator, who doesn't appear in the films, but who I think deserves merit as well, is the one that appears in the game Aliens Vs Predator (2010)
His nickname is Dark, and he's one of the most respected members of Predator society, after killing some of the most tough alien beasts in the game. He also finds the mask of an ancestral Predator, making himself a hero amongst hunters...

Well, thanks for reading, if you took the time to. I'm quite happy to have shared what I know about some of fiction's most bloodthirsty hunting murderers, and damned badass ones at that.