|Original, and best.|
The first Barbarian started as an emulation of Conan the Barbarian - an aggressive, intelligent battler, who wore little armour, entered great rages, and feared magic. They were pretty much Fighters with bigger numbers (bigger hit-dice, better abilities), which was balanced by an inability to use magical gear (too superstitious). They got some flak, but were popular enough to be carried forward into the next edition.
2e had several options - from "kits" (similar to Alternate Class Features/Archetypes) to represent a wild, bestial Fighter, through to a much watered-down version of the class. I will admit little knowledge of 2e, so I'll say no more.
Most of these were carried forward to 3rd Edition (barring the Intelligence part - most Barbarians have low, low Int scores, for whatever reason *ahem*pointbuy*ahem*). It also kick-started the mechanical "Rage", giving boni and mali when the character entered a Rage, enhancing their fighting ability but leaving them more open to attack. They turned out something closer to Berserker Warriors than Conan, but hey, horses for courses and all that.
4th Edtion changed them up a bit, but in a good way - instead of just making them really generically angry, Barbarians are spirit-channellers, calling upon the power of Primal and Elemental Spirits to batter the crap out of their enemies. Very cool, very powerful mechanically, and one of the better translations into the new "Roles" system, as it's always been a pure Striker - get in fast, smash face, RAGE, repeat until one of you is dead.
I guess they make for a weird proposition - I can imagine a whole tribe of Barbarians, but can't do that with any other class. I'd even find it weird for a Fighter's Guild to have only Fighters in it, you know? Whereas Barbarian is a Class, race and social class all rolled into one!
It makes for a very good class to add to NPCs who rely on close combat, like Orcs or Bugbears - they seem appropriate Barbarians, and taking a horde of regular Orcs and making their Champion a 5th-Level Barbarian helps keep them a threat to players. With a little refluffing, however, you can class the Rage ability as a sort of "focus", for more refined enemies - a cold fury they enter when battling, to allow them to strike down a certain target as quickly as possible.
In all this time, however? I've never played a Barbarian. Not my style, to tell you the truth. So there's another resolution - next D&D game I play, I'm playing a Barbarian. A huge, burly Viking-a-like, interested only in wenching, drinking, and battle, preferably in that order.
Wish me luck.