Unlike Emperor Palpatine, Darth Vader never seems to laugh. Have there been any offical works, including canon, non-canon, and Legends material, where (post-Episode III) Vader is shown or described as laughing?
According to canon, Vader doesn't laugh. He's not above making dad jokes, but he doesn't even crack a chuckle at his own antics.
Vader does not laugh with him. Vader never laughs. Has never laughed. Not since he was Anakin. And that is a time he dares not remember.
Moving waaaay down the canon scale, his clone is positively manic.
She never had a chance to find out. A dark figure suddenly stepped out of the shadows. The figure had broad shoulders and carried a stone ax. Tash recognized him immediately.
“Offworlder!” Maga bellowed. “Free my people!”
Vader laughed. “Another primitive savage for my labor camps.”
C-3PO: Well, you're pulling on my tummy wires.
Darth Vader: [Laughs evilly]
As so is Darth (pig) Vader from the Angry Birds game.
He laughs in Coruscant Nights II: Street of Shadows:
Sing tensed. She had no weapons, but that did not mean she was unarmed. "Are you calling me a fool— Lord Vader?"
Few people had heard the Dark Lord of the Sith laugh. When amused, his reaction as promulgated by the specialized respiratory equipment that enveloped him inclined more toward a hissing sound. But this was a real laugh, as genuine as it was humorless.
"You amuse me." He leaned slightly forward. "A rare occurrence, one that by itself justifies a portion of what the Imperial government is paying you."
(Source: Coruscant Nights II: Street of Shadows, page 146-147 of paperback edition)
And again in the novelization of The Force Unleashed:
There was no blood. Instead of pressing the attack, the apprentice stood his ground. Despite himself, he was as surprised as his former Master clearly was.
For a moment, the only sounds were the twin humming of the lightsabers and the wheezing of Darth Vader's respirator.
Then the Dark Lord laughed.
It was an awful sound, empty of humor and full of mockery. In it, the apprentice heard a decade and a half of torture and abuse.
(Source: The Force Unleashed (novel), page 309 of hardcover edition)
He also smiles in Death Star:
"We are approaching the drop back into realspace."
Vader turned and regarded the man. "And?"
Captain Pychor swallowed. "N-nothing else, my lord. I just thought to inform you."
"Thank you, Captain. I am already aware of it."
"Yes, my lord." The captain bowed, and backed away.
Inside the helmet, Vader smiled, though it caused him pain to make the expression. But pain was always with him; a little more meant nothing. It wasn't even necessary to call upon the dark side to deal with it. It was purely a matter of will.
(Source: Death Star (novel), page 50-51 of paperback edition)
I found these thanks to a thread of the same name on r/MawInstallation, and confirmed them in my copies of the cited novels.
Darth Vader does not laugh. He laughs when he is Anakin and he laughs in Star Wars the Yoda Chronicles, which is Legends, but Darth Vader never laughs in canon. He may false laugh (ha ha ha) in canon, but I cannot remember whether he does or not. But the other question is: does Darth Vader smile. Darth Vader has a mask, and so we will never actually know if he smiles. He smiles when he is Anakin, and he smiles when Luke takes off his mask, but by that point he is Anakin again.