Khornate Berserkers in both Warhammer: Age of Sigmar and Warhammer 40,000. The 40k Berserkers actually undergo voluntary lobotomies to increase their psychotic blood lust (by berserker-surgeons no less). The page quote is one of their most infamous warcries. It also helps that in regular Warhammer that Khorne's warriors tend to come from a fantasy Viking culture and is essentially an evil Odin.
Blood Angels Death Company. When they meet the above, things get really bloody, even by 40K's standards.
Kharn the Betrayer takes it Up to 11 when he attacked his own fellow World Eaters when they wouldn't fight due to the cold. He managed to so completely devastate both his army and the enemy's that both now survive only as fragmented, roving warbands.
Officio Assassinorum Eversors are this too. They undergo a series of incredibly brutal cybernetic and genetic modifications to make them more efficient killing machines, and are then pumped up on combat drugs that are both addictive to the point that they die in hours if they go into withdrawal, and would shorten their lifespan to a matter of years if they remained conscious all the time (and are effective to the point where the genetic modifications are required to boost their immune systems to avoid immediate death upon injection). To counter-act this, they're kept in cryo-pods all the time before deployment, and only awakened once they're within range of their target to avoid them going into a frothing berserker rage before time. And then they explode upon death, in case the target was not dead yet. They are, on the tabletop, one of the one model units with the most dice to roll in the attack phase.
Warhammer is no slacker, with Witch Elves, Savage Orcs, Skaven Plague Monks, and anyone else with the Frenzy special rule. One classic Skaven spell, Death Frenzy, would turn any Skaven unit into this... but they'd be so psychotic that they would rip each other to shreds as well.
Warhammer: Age of Sigmar has the Khorne Bloodbound, an entire army of frenzied berserkers that fall into this trope, all dedicated to the god of rage and murder. Special mention goes to the Wrathmongers, who have a special ability that causes not only themselves to enter a berserker rage, but all nearby allies and even their enemies, who become so engrossed in the berserker rage that they lose the ability to tell friend from foe and will just attack everyone withing range. Then there's the Blood Warriors, who will fight until their bodies are absolutely destroyed, even going as far as to take their murderers down with them. And not to be outdone is the Skullgrinder, gigantic warrior-blacksmiths who appear out of nowhere with murderous gleams in their eyes, armed with gigantic anvils on chains, and join battles using their anvils as makeshift flails while blinded by a raw murderous intent. And lastly, for anyone who isn't quite as berserked as we want,there's the Bloodsecrator, priests of Khorne carrying giant totems dedicated to the Blood God which opens a portal to Khorne's realm that, among other things,causes nearby allies to enter an unstoppable frenzy and lose all sense of preservation and any fear of pain and death.
The ultimate example of this in either setting is Skarbrand, the Exiled Bloodthirster. Having been beaten and flung across the daemonic skies for eight whole days and nights after getting the idea that he could replace Khorne by Tzeentch, he is wiped of all personality and thought beyond mindless rage. He possesses an aura that literally causes anyone around him to be filled with berserker rage, causing everyone to fight in a frenzied blood-fueled orgy whenever he appears. To top it all off, both of his axes contain mad, furious greater daemons, making him a triple berserk daemon.
The Crab Clan in Legend of the Five Rings has two distinct flavors - one set reaching a Zen-like state of rage and frequently composed of Death Seekers from the shamed Hiruma family, and the other typified by Hida Amoro, who was utterly terrifying in combat for both ally and enemy as well as being an honorless cretin outside of combat (standing out even in the rough-around-the-edges Crab Clan). The latter style of berserker generally became the only variety.
Barbarians are a play on the berserker. They wear light armor, attack with big weapons, and go into rages during battle to give themselves additional combat ability.
The frenzied berserker class prestige class goes into berserker rages on top of a standard barbarian rage. If they kill all the enemies in sight, they have to make a Will save to avoid attacking allies.
In the classic Avalon Hill WWII game, Squad Leader, shooting at Russian infantry was a dangerous pastime. If you rolled a K(ill), fine; but if you did anything BUT kill the squad, it had a chance to go berserk and ignore all results EXCEPT K, as well as vastly improved close combat abilities. Realistic? Well, it's Squad Leader, where all the streets in the villages are 40 meters wide.
Any vampire can do this in the New World of Darkness by "riding the wave" during Frenzy, entering a state where they control which targets they attack instead of just tearing crap up. One good example is the Sotoha bloodline, which grants its members the ability to perfectly hone and control their Frenzy... but having them technically be in Frenzy all the goddamn time.
The tiraks in Eon, especially the frakk, are quite (in)famous for this ability. Since tiraks are well above humans in terms of strength and endurance, they can afford to be a bit reckless.
Rifts, in its book Pantheons of the Megaverse, has a Berserker Character Class in its section on Norse Mythology. These berserkers go into their rage by stomping their feet on the ground, yelling, biting their shields, etc. This gives them combat bonuses to attack, but penalties to avoid being attacked.
The Hero System models this with the Enraged and Berserk disadvantages/complications, both of which specify a trigger condition, a trigger chance, and what dice roll it takes to snap out of that state again. (An enraged character will at least first of all attack whatever provoked them, while one who's gone berserk simply lashes out blindly altogether.) As written, this is simply pure drawback that doesn't improve the character's actual combat performance in play any (except inasmuch as having to all-out attack happens to inadvertantly help more than it hinders); to have a berserker who also gets more powerful in that state, the player would have to buy appropriate stat boosts, skill levels, and/or powers with an "only while enraged/berserk" limitation.
Clan pilots in BattleTech hurl themselves into one-on-one engagements with reckless abandon, though their generally superior equipment lets them get away with it frequently. Amusingly, their disdain for actual melee combat (and their silly code of honor) meant that many a warrior were killed when their cockpits were crushed by battlemech punches from the much more pragmatic Inner Sphere pilots. Solahma warriors - "old" Clan warriors considered past their prime - are thrown into the field as Cannon Fodder, often with nothing more than an outdated rifle and a flak jacket, and are expected to charge the enemy and inflict as much damage before inevitably being gunned down.