In Warhammer 40,000, the stories and legends about the Primarchs, semi-mythical figureheads of the Space Marine legions, and the Emperor nearly all involve some establishing moment from the Primarch's first actions after being born (normally slaughtering hordes of aliens) to the first meetings between the Emperor and the Primarchs which will say something important about how they saw him or why they betrayed him.
"Konrad Curze. I have come to take you home. "I know what you are going to do. And that is not my name. I am the Night Haunter."
This is the meeting between the glorious shining emperor and the Primarch who essentially ends up commanding a legion of genetically engineered super-terrorists, and is also essentially 40K's Batman.
Leman Russ of the Space Wolves has a real gem in his origin story. After he defeats the Emperor at eating and drinking contests, he fights him bare hand to Emperor's unrivaled armour and Power Fist, which are the absolute zenith of human war tech, and possibly the greatest pieces of wargear in the history of the universe, and punches him across the room. Then laughs it off when he gets beaten.
The earliest specific anecdote from Horus' backstory is mention of how the Emperor saved his life in one battle, then he went on to save the Emperor's life in a later one, establishing the close bond between the two and establishing Horus as a warrior of near the Emperor's caliber.
Vulkan's first mention is an incident where instead of hiding from the Dark Eldar raiders like people on his homeworld normally did, he stood in the square with his hammers and waited for them to come, inspiring the people of his village to stand with him; foreshadowing the Salamanders' role as one of the more heroic Chapters with a significantly greater regard for the average citizen of the Imperium than most.
Fulgrim started out on a very resource-poor world, and managed to increase the efficiency of the economy to the degree that he could foster a renaissance of art and culture, establishing his great appreciation for the finer things in life and setting up the means of his downfall.
Magnus the Red first met the Emperor telepathically and the two conversed in the Warp for a long time before meeting in the flesh, foreshadowing Magnus' great psychic power and the means by which he fell.
Sanguinus bent knee to the Emperor immediately upon meeting him, in stark contrast to those who resisted, alone among the Primarchs exhibiting the virtue of humility.
Lorgar is introduced preaching the word of the Emperor upon receiving visions of his arrival, then starting a religious war and destroying the old doctrine, foreshadowing his role in the schism to come.
Alpharius first appeared when he posed a serious threat to Horus' battlefleet with a force of primitive one- and two-man fighters, then refused to explain where he came from, foreshadowing both his Legion's love of fighting guerrilla wars from the shadows using inferior forces and their penchant for secrecy.
Those immortal words printed on the front cover of the rulebook: In the grim darkness of the far future, there is only war.
The longer opening narration from both Warhammer and Warhammer40000 in general, containing such lines as "For there is no peace amongst the stars, only an eternity of carnage and slaughter, and the laughter of thirsting gods."
In Exalted, the titular Exaltation often serves as an introducing character moment given that it, you know, gives its Chosen the power to slay gods and changes their life forever.
A particularly good example of this is in Sesus Nagezzer's backstory, shown in the Aspect Book: Wood. Before Exalting, he was just a bookish teenager, sitting down and reading a book on war tactics, nibbling a cookie. And then his bullying elder brother shoved him into a fountain. Nagezzer's response was to start channeling Essence and kick his ass...though not before calling him out on his idiocy and general failure in a very intelligent, verbose way that you wouldn't expect from a teenager.
And throughout his life, Nagezzer is defined by his genius intelligence, his dedication to ethics and the tradition of the Realm...and his love of sweets and general luxury, which is a major flaw that he constantly struggles with.
Another example is Rafara, who Exalted after seeing her mother throw Rafara's nannies- the only people she'd had any positive emotional contact with- into a sea of hungry sharks. That alone should tell you how traumatised Rafara is...and why her main motivation is to kill her mother.
DM's out there, pay attention. This is critical. Every time you introduce an NPC, think about the exact impression you want to give your players. This is true for any game, whether is be GURPS, Dungeons & Dragons, Shadowrun...any tabletop RPG.