Historically, a Bounty Hunter is someone who captures or kills a particular person for money (the "bounty"). The practice is distinguished from that of an Assassin by the target being an outlaw and a preference for taking their target alive.
Bounty Hunter is a Slayer archetype that trades medium armor and heavy shields for some exotic non-lethal weapons. Certain talents are traded for abilities that make them good at dirty tricks, grappling and non-lethal damage. It's actually one of the better options for focusing on Dirty Trick, which itself tends to be the best combat maneuver option due to lack of things immune to it and the potency of ailments it can cause.
An archetype that any class can take to track a target. Grants the ability to track any query like a ranger, and gain bonuses and proficiency to non-lethally catch your pray. Feats are: Additional bonuses when using Hunt Prey action(more if you already had it), party gains bonuses for helping you look, gain proficiency with bola, sap, and whip (no-penalty to non-lethal), Quarry can't shake you off if they move in combat, and can grapple if Quarry critically fails a sword attack.
Next to soldier, and smuggler, Bounty Hunter is easily among the most recognized character profession in Star Wars due to the cool looking bounty hunters (who ultimately don't actually do anything aside from Boba Fett, who dies to a blind man) in Empire Strikes Back being addressed by title and being implied to be more adept than the best the Empire had to offer instantly led to them being cool. A combination of people missing the fact that the Empire is the government, meaning a bounty on a recognized outlaw like Han Solo is a legitimate law enforcement practice, and that Boba Fett's turns around and double dips by selling Han in Carbonite to a recognized criminal overlord has resulted in Star Wars "bounty hunters" being more mercenary special forces units to anyone who is willing to pay than the freelance criminal hunters.
In game terms, the title "bounty hunter" tends to suit most groups of player characters that aren't actively fighting for or against a particular government and instead act like high fantasy Adventurers IN SPACE.
In Star Wars d6, there's over half a dozen templates with "bounty hunter" in the name and more that assume the profession without having the name in their title. Some bounty hunters were recurring foes in the various published modules.
In Star Wars D20, Bounty Hunter is a core Prestige Class. It has a scaling favored enemy against a single person chosen at the start of the session and full sneak attack progression on a full BAB chassis with all medium saves and good skills. It's fine only because of the strength of full sneak attack on such a good chassis than actually being well designed.
In Saga Edition, Bounty Hunter is again a core Prestige Class. Here it's notable for the ability to take the Hunter's Mark talent from the Bounty Hunter talent tree. This talent is absurdly good, decreasing the condition track of any target that is hit after the aim action is taken while stacking with itself, is a critical part of the "Condition Track Killer" build that stands as one of Saga's more broken builds.
In the Fantasy Flight Games system, "Bounty Hunter" is one of the profession options for Edge of the Empire.
Like Star Wars, "Bounty Hunter" in Metroid pretty much just means "Elite Space Mercenary". Supposedly, Nintendo of Japan was so oblivious as to what the term actually meant they were horrified when Retro Studios planned to include a system of optional objectives around taking out specific criminal targets.