The definitive example for the whole setting may very well be Sigmar Unberogen uniting the tribes of men and joining forces with the Dwarfs of Karaz-a-Karak to hold back a massive Orc horde at Black-fire Pass. Not only did Sigmar personally slay the Orc Warboss, but the entire battle in general stood as a sterling example of the importance of unity, as it was only through banding together that the tribes of the Reik basin were able to survive the onslaught. Had they been living as they were before the Unification, they would have been destroyed. It was not only the ultimate triumph of Sigmar's strength, but also his ideals. With the end of the battle, any doubts the tribes had of Sigmar were erased and they gladly accepted him as their ultimate leader. In this battle, Sigmar earned his titles; "the Hammer of the Orcs", and "the Anvil of the Dwarfs".
Hell, anything and everything Sigmar does in general counts. The guy was made of pure awesome.
Getting crowned Emperor of the lands of men by the Ar-Ulric, anyone? Such a glorious moment that it is celebrated annually by Imperials on the 18th of Sigmarzeit. It was also the day he abdicated the throne to fight Chaos in the east.
Killing a Bloodthirster of Khorne in single combat (well, with some Divine Aid) and banishing it back to the Realm of Chaos.
Chasing a fucking Lord of Change all the way back to the Realm of Chaos also. Sigmar scared the shit out of a LORDOFCHANGE.
Engra Deathsword, during the Great War of Chaos. This towering Norsecan Chaos Champion was a general in the armies of Asavar Kul and led the extermination of the the city of Praag. His sheer brutality was SO great that he caused the very city to mutate and those mutations wailed in agony as the saw the horrific punishments Engra meted out against those who dared challenge him. Engra is fucking proof that you can have a Finnish woman name and still be completely badassed.
Archaeon claiming the six treasures of Chaos: And Warhammer is supposed to be a Low Fantasy setting!
Singlehandedly slaughtering hundreds of monsters in total darkness so deep it instantly snuffs out any light, all while climbing the interior of a tower so tall it seems to pierce the moon, then sacrificing their hearts on an altar at the very top to receive his Mark of Chaos.
Destroying an entire city and killing every last occupant in a battle that lasted six days and nights, then battling the ghost-animated, Nigh Invulnerable Armor of Morkar the Uniter to a standstill immediately thereafter. He wins by calling out to Morkar's spirit in the dead tongue of the Unberogen, the language of Sigmar himself in life, and promptly cutting him down. Then he takes the armor and wears it himself.
Walking right up to a monstrously huge Chaos Dragon called Flamefang, waking it up by slamming his axe into the dragon's head, then killing it singlehandedly by being swallowed whole and then hacking his way out from inside, all to recover the Eye of Sheerian.
Going to the Realm of Chaos and sneaking inside the fortress of a Daemon Prince to steal away with The Steed of the Apocalypse, then breaking the daemonic beast's will to make it accept him as a rider.
Recovering the ancient sword of Vangel the Second Everchosen, the Slayer of Kings, from the fist of Krakanrok the Black, a Dragon Ogre the size of a mountain.
Claiming the Crown of Domination, which involved, in order, overcoming Nurgle's most potent plagues, navigating a crystal labyrinth created by Tzeentch whilst blindfolded, resisting temptations sent by Slaanesh itself, and finally dueling with a Bloodthirster and killing it singlehandedly, which he achieved by disarming it and throttling it to death with its own whip.
The saga of the Gorehunt tribe, which was given in the 7th edition Chaos codex by Phil Kelly. The Gorehunt were a tribe of Norsemen dedicated to Khorne who vowed to travel to distant lands and offer up the skulls of enemies of many stripes to their god. So they took to their longships and sailed to Araby and, to use the vernacular, fucked shit up. The Emirs had to send armies of thousands, and hundreds of thousands to defeat the blood crazed Norse, and all those armies who absolutely slaughtered. Now, this seems awesome by itself, but keep in mind that the Norscans were only a hundred in number. These champions of Khorne were annihilating armies several times their numbers. The Norscans carved through the armies with such abandon that a raging stream of blood began to flow through Araby and still does. Even arcane creatures couldn't stop the warriors of Khorne; and simply caused their killing frenzy to grow. Finally, the Emirs sent, as the story put it — "gigantic beasts of war, and armies that hid the dunes with their number", and the Norsemen's last stand was a glorious one. And the river became larger and larger, and though the Northmen were eventually killed, they had defeated armies that dwarfed them utterly and pleased their master, for the crimson river still flows through Araby in testament to their skill and sacrifice. Seriously, there hasn't been another story that truly encompasses the badassery of Khorne as this one does, Phil couldn't have chosen a better one to put in the codex.
There's a story in the 8th ed Warriors of Chaos armybook about a Norseman by the name of Borkill the Bloody-Handed who was hunting a Bonegrinder Giant (for the uninitiated, that's giant whose unto a giant as a giant is unto a human) throughout Skaeling tribal lands. At the base of a jet black monolith he finds a chalice filled with a dark liquid. As he drinks from the cup, the giant attacks, and Borkill's body begins to swell with power and he manages to defeat the giant in a straight-up, one-on-one battle. In awe of this, Borkill's fellow Skaelings build a giant, blood-red Chaos monolith commemorating his deed.
Another one from the eight edition armybook is the tale of the Chaos Lord Ragnar Painbringer, who attempted to invade a major Wood Elf holding. Of course, Wood Elves being Wood Elves, the trees come alive and attack the warband, and the elves themselves pound them with arrows from afar, killing many. Eventually, Ragnar looks upon this and says "fuck this, bring up the Gorebeasts", and thus did the Northmen bring up the Gorebeast Chariots. Basically like normal chariots, but pulled by hulking Chaos-mutated rhinos. The chariots charge, the elves die, the trees splinter, and the Chaos Warriors, brimming with Viking rage rush into battle, slaughtering the stragglers with Ragnar at the fore.
Grimgor Ironhide defeating Archaeon, the single strongest warrior of Chaos, in single combat.
Settra, an immortal mummy, fighting against Nagash, who just consumed the Nekaharan god of the Dead and became one himself. Even though the former lost the battle, he is still defiant to his last breath, and may be coming back for round 2.