In Harry Potter and the Half-Blood Prince, after drinking the potion from the basin Dumbledore starts having hallucinations or nightmares.
Do we know what he saw? Why was he crying?
He was seeing (a nightmare version of) the night Ariana died.
Harry gives his thoughts on this during a discussion with Aberforth in Deathly Hallows (thanks to @chirlu for the keyword, saved me a search!).
"He was never free," said Harry.
"I beg your pardon?" said Aberforth.
"Never," said Harry. "The night that your brother died, he drank a potion that drove him out of his mind. He started screaming, pleading with someone who wasn't there. 'Don't hurt them, please . . . hurt me instead.' "
Ron and Hermione were staring at Harry. He had never gone into details about what had happened on the island on the lake: The events that had taken place after he and Dumbledore had returned to Hogwarts had eclipsed it so thoroughly.
"He thought he was back there with you and Grindelwald, I know he did," said Harry, remembering Dumbledore whispering, pleading. "He thought he was watching Grindelwald hurting you and Ariana...It was torture to him, if you'd seen him then, you wouldn't say he was free."
If we look at some of what Dumbledore said in Half Blood Prince, this fits pretty correctly.
"Its all my fault, all my fault," he sobbed. "Please make it stop, I know I did wrong, oh please make it stop and I'll never, never again ..."
"This will make it stop, Professor," Harry said, his voice cracking as he tipped the seventh glass of potion into Dumbledore's mouth. Dumbledore began to cower as though invisible torturers sur-rounded him; his flailing hand almost knocked the refilled goblet from Harry's trembling hands as he moaned, "Don't hurt them, don't hurt them, please, please, its my fault, hurt me instead ..."