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.
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.