Sammael

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 Crowley and Azazel. 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.
Memory Extraction - By inserting part of her essence into her victim, Abaddon could access their memories (even their subconscious memories) and gain information about what they had seen and heard.
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.
Special Abilities when making deals with mortals
Healing - In the context of a deal, crossroads demons can heal themselves and others of any wound as demonstrated by Azazel and Crowley. While in Hell, demons such as Alastair can heal any wound applied to their victim, so that they can continue to torture them again and again.
Reality Warping - Crossroads demons, and a few other Demons can grant humans a wish in exchange for their souls. It is worth noting that Azazel did not need to take souls, and could grant wishes from his own power, which he did in exchange for permission to enter the homes of special children, on their 6-month birthday. Lilith also claimed she could make deals without taking a soul but this was never confirmed. While in Hell, demons can alter reality to torture people in ways that are beyond human imagination. One of the reasons Alastair despises being on Earth is because reality is "too concrete" and there are too few resources for torturing people effeciently.
Resurrection - One of the wishes demons can grant is the resurrection of a loved one. Crowley claims that, since he is now the king of Hell, he is strong enough to resurrect anybody in his care without a deal. He demonstrated this by resurrecting Samuel Campbell in Season 6; the 'patriarch' he 'took off the bench' in order to capture Alpha creatures, which Crowley hoped would lead him to the door of Purgatory. Azazel also displayed resurrecting, the young John Winchester after he killed him, in the context of a deal. He couldn't however resurrect Dean (possibly because he hadn't crossed over yet)- instead, he possessed a Reaper, who he used to do it for him.
Shapeshifting - Demons can take any form they wish while in Hell. Several demons were able to take the appearance of Sam and Dean while torturing Bobby Singer in Hell.

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 demons from using their powers. 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.
Salt - Demons are unable to cross a line of salt and can do very little to damage the line at all. They cannot open doors lined with salt if opening it would break the line. Salt can also be used to torture demons by making them ingest it or by injecting them with saltwater. Forcing a Demon to ingest salt will drive them out of their host. It can also be put into shotgun rounds to hurt and knock back demons. However, Azazel is immune to this weakness and Crowley was hardly affected by rock salt shots, but he still found the experience painful.
Holy Water - Holy Water burns demons that come into contact with it, like acid (though it does no damage to the human host, only the Demon). It has proved to be very effective against demons, as only Azazel and Lilith have been thought to be immune to it. However, certain high-tier demons seem to develop some resilience to it as Ruby practically laughed when Sam was about use it against Alastair because it would barely slow him down and, while it caused them pain, it only affected Crowley and the Seven Deadly Sins for a very brief period of time.
Iron - A demon can't touch iron without its skin burning or cross it if it is used to erect a barrier, much like salt. Samhain and Alastair were immune to this weakness and Astaroth had some resistance to it. In large groups, Demons are able to overcome this weakness, as the Demon army was able to break an iron Devil's Trap in order to escape.
Palo Santo - Basically a wooden, hybridized version of salt and holy water. When a demon is stabbed with it, it causes the wound to smoke and painfully pins the demon to a single spot, immobilizing them long enough to perform an exorcism. Palo Santo isn't commonly used by many hunters due to the fact that it damages the hosts the demons are possessing. (The Magnificent Seven)
Flesh Sigil - By carving a particular sigil into a demon's possessed flesh, it is possible to lock the demon within its host and disable its powers, the most important one being teleportation. However, demons with these sigils are not bound to a single place and can roam around freely if not restrained by some other means. (The Devil You Know)
Holy Fire - Though not fatal to demons as it is to Angels, Holy Fire can cause demons extreme pain, as demonstrated when Castiel threw Meg into Holy Fire (Abandon All Hope...) and when Sam doused Abaddon in Holy Fire, causing her so much pain she fled both the scene and her vessel (Sacrifice).
Purified blood - The blood of a person who has confessed his/her sins is shown to be able to hurt demons if injected into them.