Death himself might possibly exist because supposedly Beedle the Bard witnessed The Peverell brothers defy Death. After seeing the brothers cross a treacherous river using magic they were confronted by Death who then gave them the Deathly Hallows.
http://harrypotter.wikia.com/wiki/Death_(being)
The being known as Death is the embodiment of the universal phenomenon
marking the end of physical life, and may or may not literally exist.
The best–known account of the entity is known as "The Tale of the
Three Brothers", and was made famous Beedle the Bard. According to
this story, he was the one who witnessed the three Peverell brothers
defy him by successfully crossing a deadly and dangerous river using
magic.
Quotes from the book
“There were once three brothers who were traveling along a lonely,
winding road at twilight. In time, the brothers reached a river too
deep to wade through and too dangerous to swim across.. However, these
brothers were learned in the magical arts, and so they simply waved
their wands and made a bridge appear across the treacherous water.
They were halfway across it when they found their path blocked by a
hooded figure.
And Death spoke to them. He was angry that he had been cheated out of
three new victims, for travelers usually drowned in the river. But
Death was cunning. He pretended to congratulate the three brothers
upon their magic and said that each had earned a prize for having been
clever enough to evade him."
Harry Potter and the Deathly Hallows, Chapter Twenty-One
Now the reason in this story that Death created the Hallows to begin with was to claim the wizards that cheated him from claiming them.
The oldest brother was claimed after he defeated a wizard in a duel then boasted in an inn, in which at night he was killed by somebody who wanted the wand.
"That very night, another wizard crept upon the oldest brother as he
lay, wine-sodden, upon his bed. The theif took the wand and, for good
measure, slit the oldest brother’s throat.
And so Death took the first brother for his own."
The second brother killed himself after discovering that though he could bring back the woman that he wanted to marry she was not supposed to be in this world and was cold and suffering.
"Yet she was sad and cold, separated from him as by a veil. Though she
had returned to the mortal world, she did not truly belong there and
suffered. Finally the second brother, driven mad with hopeless
longing, killed himself so as truly to join her.
And so Death took the second brother for his own."
The last and youngest brother lived to old age because he hid from Death, then gave the cloak to his son and joined Death.
"But though Death searched for the third brother for many years, he
was never able to find him. It was only when he had attained a great
age that the youngest brother finally took off the Cloak of
Invisibility and gave it to his son. And then he greeted Death as an
old friend, and went with him gladly, and, equals, they departed this
life.”
The only reason I think it might be plausible that Death exists is in this story each Brother was given an item that would eventually lead them to their death so that Death would claim them.
On the flip slide there is no concrete evidence that Death exists as a physical manifestation. The only thing that can be said is that Dumbledore thought that the brothers themselves created the artifacts and that the story was embellished.