In the Mystara setting (formerly known as Basic-Expert-Companion-Master-Immortal D&D), the four cardinal elements are associated with the four Spheres of Life. Along with the Spheres of Entropy, they make up the Spheres of Power that empower the Immortals.
Fire: Energy, creativity, intelligence, magic, mages, chaos
Water: Time, wisdom, clerics, neutrality
Air: Thought, trickery, dexterity, thieves, good
Earth: Matter, strength, fighters, resistance to change, law
There's also the Tarot card associations:
Fire: Wands, male fertility, power, will, passion, ingenuity, inspiration
Water: Hearts, cups, female fertility, emotions, sensuality, temptation, love
Air: Swords, intelligence, death
Earth: Diamonds, pentacles, coins, health, money, charity, bounty, groundedness, dedication, wealth, success
The negative quasielements are all associated with Entropy. In Mystara, Entropy is linked to evil, undeath, and the destruction of the Spheres of Life, opposing all the concepts they represent or offering dark, twisted equivalents of them.
Dust: dissolution, disintegration, the opposites of everything Earth stands for.
Vacuum: Suffocation, strangulation, nothingness, endings, the primal void that contains nothing and everything, writer's block, the opposites of Air.
Salt: Infertility, barrenness, the opposites of water.
Ash: Enervation, cold, anti-magic, illiteracy, the opposites of fire.
The positive quasi-planes are a bit weird. For me the associations aren't very closely related to the cardinal planes connected with them.
Steam: the primordial mists, the first breath, the Ginnungagap, Ymir, the frost giants, Odin, Villi, and Ve, "magical (and creative) power-filled space," the liquid, deadly, substance of life, primal chaos, Auðumbla, sleep, deception.
Lightning: the first spark, the fire stolen from the gods, the coming storm, the sky-god, king of the gods, the paternal, fertilizing force.
Mineral: the first tone, the sound from which the multiverse formed, music, the primal earth, mother of the gods, the maternal, fertile force.
Radiance: the first rays of light, the birth of the sun, the dawn of all things, the sun-god, the awakening force, the end of dreams, the enemy of primal chaos, the enemy of dreams, blindness, truth, justice.
The paraelements represent extreme parts of the world, where the four seasons go to dwell when they're not active.
Ooze: Garbage, trash, refuse, silt, the bottom of oceans, the deep muck where all things fall and collect and strange blind things lurk, claiming everything that falls into their domain for their own, grasping, patient, pitiless, alien greed that never lets go, scavengers, dumpster divers, recyclers, "Human Occupied Landfill," Jabba the Hutt, spring.
Magma: Heat, the fire in the heart of the world, the magnetic dragon that lives in the Earth's core, the beast that shouted love at the heart of the world by Harlan Ellison, deep magic, deep deadly earthmagic practiced by dwarflike forgemasters who create bad luck for those on the surface, the intoxicating volcanic fumes of prophets and sibyls, monsters that sustain the world but, if freed, would destroy it, restrained love, restrained passion, the long-forgotten fires of creation still burning in their earthy prison, necessary evils, buried sins, the tortured whale that holds up the world, prison labor, slavery, summer
Smoke: poisonous gases, choking, the trenches, the smoke of war, the war between air and fire, the war between intelligence and wisdom, the war between pragmatism and idealism, the war between bureaucracy and imperial power, the war between tradition and radicalism, incense, smells, hallucinogenic fumes, narcotics, other mind-altering smokes, ritual sacrifice, masks, concealment, disguises, veils, ambiguity, spies, double agents, messages to the gods, gifts, alien worlds with alternative atmospheres, masked aliens with ambiguous agendas, autumn
Ice: Glaciers, Niflheim, magnetic north, the electromagnetic tree that binds the world, ice planets, the rebel base at Hoth, snow, sleet, rain, preservation, frozen hearts, the stilling of emotion, hunters, caribou, the Wild Hunt, the North, the North Wind, winter, eternal winter, the White Witch of Narnia, and this:
They built the frozen house to host the souls of their dead, to keep them safe until they are needed again. They made it a place of crystal and ice so cold that neither soul nor memory could dissipate or become lost in the wild Planes beyond. They made the plane a puzzle-box of shining chill to keep their best and greatest hopes in one place until the danger arrives.
Then the danger finally came, and it wasn't what they thought it was at all. It wasn't interested in them, only in the souls themselves. It was the celestials, and no one thought it would be them. The angels called them jailers, misers, thieves. They took away the souls who were their guardians and they even took away the cold so they couldn't save any more. They took winter away, and now they weep in the endless summertime, naked and afraid.
I only associate the concepts already provided in the canon. Which I believe I already mentioned earlier.