(Pictures not mine, will removed if asked)
Personality
Due to his advanced age, Death is completely detached from the rest of the universe. He cares little for major events of the world like the Apocalypse, and despite his coerced involvement by Lucifer, he only pays the events vague interest. Unlike his siblings, Death is shown to have a more civil and calm manner when dealing with the other beings. Death also claims to be an acquaintance of God Himself, claiming that the two both share a similar advanced age to one another and that neither of them can remember which is older any more. Despite being callous at times, Death has a respect for the natural order of the universe.
Death himself does not normally resurrect people (most likely because it disrupts the natural order) though he can make exceptions. Unlike the other Horsemen, Death has a level of respect for humans, specifically the human soul. Death tells Dean that the soul is stronger than anyone knows, and that it can suffer much and be broken but can't be destroyed, not even by him. However, Death is mum as to why the souls seem to be so important.
Despite claiming to be totally indifferent to humans and Earth, Death has helped on a number of occasions. It is implied that he is not so much uncaring as he is above the petty struggles of the world, disliking being called on to fix things that he thinks should have been taken care of without bothering him.
Death also has an appreciation for human food, especially junk food. His liking for Chicago's pizza was so strong he noted it as the reason he spared the city. Later, when Dean summoned and bound him, he brought him pickle chips in an attempt to appease him, which proved fruitless; nonetheless, after he was unbound, Death ate the food anyways and expressed his enjoyment of them on his way out.
Powers and Abilities
As the eldest Horseman, Death is an immensely powerful being, possessing incalculable power and near-omniscience. He is the most powerful being the Winchesters have encountered and faced, far exceeding all others, even archangels, Leviathan and even the Mother Of All Monsters , the only being known to match his immense power is God .
Memory Manipulation - Death is able to suppress memories of those he comes in contact with. It is notable, however, that this is not permanent, and would eventually fall.
Invulnerability - As a Horseman, and a fundamental, driving force, Death cannot be physically destroyed.
Immortality - He's truly immortal and doesn't age. As such, he is not affected by death, disease, pain or fatigue. He claimed to be the only being to last forever.
Resurrection - As who he is, Death can resurrect anything and anyone he wants, simultaneously. However, he chooses not to as it bends the Natural Order.
Nigh-Omnipotence - He's called a "fly swatter" by the angel Castiel, inferring that everything he reaps, is a "fly" in comparison. Death can do practically anything, from creating a lunar eclipse, to going to Lucifer's Cage, without its key, in a matter of seconds. He made his own scythe turn burning hot, without even looking at it. He is capable of killing anyone or anything in Creation, ranging from humans to archangels. Death has also claimed he will reap God in the end.
Nigh-Omniscience - Having existed alongside God since the beginning of time, Death has an extensive knowledge, including information about the universe, created beings and souls. However, Death is not all knowing as he once admitted that neither he nor God can remember which of them is older or even if they are the same age.
Teleportation - He can teleport himself anywhere in the universe instantly, although he's not Omnipresent like God is.
Weather Manipulation- Death is able to conjure, create and muster tsunamis, tornadoes, hurricanes, and thunderstorms he even caused the Great Flood. As Lucifer asked him to, he was going to wipe out an entire state with massive weather anomalies, but later decided not to.
Killing Touch- He can kill anything in this manner. When brushed by a mortal, the man died.
Invisibility - Like his brothers, Death can only be seen when he wants to be seen.
Superhuman Perception - He can tell what something truly is, regardless of how it appears, or if it is invisible.
Apporting - Death was able summon his scythe to him.
Terrakinesis - Able to make whole areas violenty shake, for instance when he was released, or when he was bound.
Thermokinesis - Caused his scythe to heat up simply by thinking it.
Weaknesses
Even Death itself/himself has a few minor weaknesses. Death can effectively be bound. God himself kept him imprisoned beneath the Earth surface for thousands of years. After raising him, Lucifer was able to bind Death to his presence and control his actions to a moderate degree. Although Lucifer bound Death to serve him during the apocalypse it does not prove that Lucifer an Archangel can overpower Death, even a mere human can bind Death with the right spell.