Asmodeus

Demonic Possession - Like angels, most demons (only known exceptions are Acheri, Daeva and Hellhounds) require a human vessel or "meat suit" to travel on Earth. Unlike angels, they do not need a person's consent. Also, unlike angels, demons can possess corpses. It is easier to take control of people who are in states of heightened emotions or fear. They can also access their host's memories while possessing them (even if it is a brief possession). This ability can be thwarted by Anti-possession tattoos. Also under certain circumstances, the person being possessed can regain control if his or her will is strong enough. They can also possess humans who are already possessed by an angel (and probably by another demon), but the only problem is the angel can neutralize it, because angels are naturally stronger than demons. In many cases, the demon will ride the host hard for fun and once they vacate the host will die.
Electromagnetic Interference - Demons, like spirits, often disrupt nearby electronics with their presence. Large number of demons can cause thunder storms.
Flight - Only when in their natural forms.
Immortality - Demons have an indefinitely long lifespan and an arrested aging process.
Invulnerability - Injuries that would be fatal to humans, such as broken necks or gunshot wounds, have very little - if any - effect on demons. They can only be killed by special weapons or rituals. Unlike angels they don't always heal their vessels. If the "meatsuit" receives too much damage they simply find another human to possess, leaving their former vessel to die.
Super stamina - Demons never tire, and do not require food, water, oxygen, or sleep to sustain themselves. Sam states that they also do not get hot or cold and Dean states they do not need to urinate.
Super strength - Demons possess superior physical strength compared to that of humans; capable of physically overpowering humans. Demons can also overpower most monsters. Once, a demon (the Phantom Traveler demon) ripped open an airplane hatch with over 2 tons of pressure at over 1,000 feet above the ground. The higher ranking the demon, the stronger it is. The highest ranking demons can overpower low-level angels.
Supernatural Perception - Demons are able to see hidden supernatural activity and beings, such as Reapers, ghosts, and Hellhounds.
Supernatural Senses - Demons have an enhanced sense of smell and taste, demonstrated as Crowley could identify Castiel was in Dean's Impala and that he and Raphael had been using dog's blood.
Telekinesis - Demons can move or suspend objects and other beings with their minds. Higher ranking demons can use this ability to pin their victims to walls or kill people by snapping their necks.
Soul Extraction - Demons have the ability to forcefully remove a person's soul from their body.
Biokinesis - Some demons can manipulate the biology of other beings. Azazel, for example, was able to torture Dean by causing him to hemorrhage. Meg was also able to cause Crowley to cough up blood in a similar manner. Astaroth stopped Elizabeth's heart with a wave of her hand and Abaddon caused people to bleed from their eyes. Crowley was even able to cause a girl to explode by snapping his fingers.
Electrokinesis - Displayed by Azazel and Crowley. They could manipulate electronic equipment to their will. Also the demon possessing Isaac's corpse was able to switch on an old radio.
Invisibility - Some demons can become invisible to humans.
Pyrokinesis - Some demons can generate and manipulate fire. Azazel, Abaddon and (probably) Brady have demonstrated this ability. Crowley can also manipulate fire; he extinguished a Holy Fire circle by snapping his fingers, and also pretended to set himself on fire.
Soul Reading - Some demons, particularly Crossroad Demons, can assess the condition of one's soul.
Spell Casting - Some demons can practice witchcraft, much like witches, like altering the range/space they occupy. Other demons are adept in Enochian magic which they use to protect themselves from Angels. Alastair knew of a spell that could allow him to banish an angel back to Heaven. Meg and Casey knew of spells that they could use while inside a Devil's Trap, allowing them to break free.
Teleportation - Some demons can travel from one place to another instantly, without occupying the space in between.
Terrakinesis - Limited; Some demons can create small earthquakes. This was once used to destroy a Devil's Trap drawn by Kevin Tran. (We Need To Talk About Kevin)
Thermokinesis - Certain demons such as Lilith and Crowley can emit great heat through their skin resulting in severe burns to whatever they touch. Crowley also once caused Ruby's knife to burn red hot by merely snapping his fingers, forcing Dean to drop it. (We Need To Talk About Kevin).
Healing - Used by Crowley, he is the only demon who has shown the ability to heal others out of the context of a deal, albeit a small wound. (All Dogs Go To Heaven) Being a high-level demon, Asmodeus has the ability to heal.
Weather Manipulation - Some demons such as Meg and Father Gil are able to alter the weather to a limited extent such as creating sudden gusts of wind. More powerful demons like Azazel can create stronger winds and Abaddon could trigger thunder and lightning merely by screaming.
Regeneration - At least some demons can heal their hosts from any physical injury they sustain. Meg was able to heal several broken bones after falling from a window. Crowley, Meg and Ruby have all been shot on several occassions and show no signs of injury following the incident. Crowley has also healed his vessel after being severly burned by an angels white light and being stabbed throught the shoulder by an angel blade. However, after leaving their host, any injuries the body has sustain reappear and the host dies. Oddly, while Crowley has vacated his vessel several times, many of his injuries (such as his burns) did not reappear on his host (though his host seems to have died so it is possible some of his injuries did reappear).
Access to/from Hell - High ranking demons such as Azazel, Alastair, and Crowley can easily teleport themselves back and forth between Earth and Hell, without the need for any complex summoning ritual or assistance. This however, varied among high-tier demons, as some were kept imprisoned due to unknown reasons and methods.
Dream Walking - Displayed by Azazel only on the special children. He could enter and control the dreams of his targets.
Mind Manipulation - Displayed by Crowley only, he was able to grant his illiterate son the ability to read simply by touching his head.
Enhanced Immunity - As a general rule, the more powerful the demon, the more resistant they are to harm and common anti-demon methods such as salt and Holy Water. High ranking demons like Alastair are immune to the Killing Touch of normal angels and both he and Abaddon are immune to the killing effects of the Demon-killing knife though it causes them pain. The Knights of Hell could only be killed by the First Blade and Cain, the original Knight, is completely immune to the knife to the point it doesn't even hurt him.
Memory Manipulation - Displayed by Abaddon, Crowley and Azazel. Abaddon was able to read the memories of individuals, Crowley stated that he "scrubbed" Kevin's short term memory and Azazel was able to erase Dean's memory of his conversation with Tessa. (In My Time of Dying)
Summoning - Displayed by Samhain. He could summon and control various monsters, ghosts and zombies.
Exorcism - Displayed by Abaddon and (possibly) Lilith. She forced a demon out of its host and back to Hell by choking its vessel. Lilith also claimed that she sent Ruby to Hell and then possessed her vessel.
White Light - Used by Lilith (Jus In Bello, No Rest for the Wicked) and Samhain (It's the Great Pumpkin, Sam Winchester). High ranking demons can use this to generate massive amounts of destructive energy that can obliterate large areas. This ability is extremely rare and are otherwise present only in the more powerful angelic beings.
Demonic Smiting - Cain, one of the first and most powerful demons, displayed the power to smite other demons similar to angels, but with a red glow rather than a white one.

Devil's Trap - A Devil's Trap will hold a demon in place and prevent its escape. No matter how powerful the demon is, they are bound by the Trap. The Trap will also prevent low-level demons from using their powers, though Castiel's Enochian circle was able to completely bind even Alastair's abilities. It also locks a demon inside its host unless it is exorcised. For some reason, a demon inside a trap is usually unable to do anything to damage the integrity of the circle, which would allow its escape. A Devil's Trap engraved into a bullet and shot into Abaddon's head was shown to limit her movements like a normal Devil's Trap would and to bind her to the body she was possessing.
Death - Death can reap anything in existence, including demons, reapers, monsters, angels, and gods.
God - Being omnipotent and omniscient, God can kill any demon He so desires.
The Colt - Much like Ruby's Knife, it will kill any demon that is shot while within a host if the shot is a fatal one. It is more powerful, however, as it affects upper level demons as well, even when the Knife does not. Though it may not kill demon lords, it is still very painful to them.
Angel/Archangel Blade - While the angel blade is mostly just incredibly maiming and painful, an archangel's blade can kill demon lords.
The First Blade - The First Blade, combined with power from the Mark of Cain, is capable of killing demons that even other weapons can't such as the Knights of Hell.