Laughing is just a normal activity of Lord Shiva as discussed in a passage of Mahabharata which I discuss here:
He has snakes for his belt, and his ears are adorned with ear-rings made of snakes. Snakes form also the sacred thread he wears. An elephant skin forms his upper garment. He sometimes laughs and sometimes sings and sometimes dances most beautifully. Surrounded by innumerable spirits and ghosts, he sometimes plays on musical instruments. Diverse, again are the instruments upon which he plays, and sweet the sounds they yield. He sometimes wanders (over crematoria), sometimes yawns, sometimes cries, and sometimes causes others to cry. He sometimes assumes the guise of one that is mad, and sometimes of one that is intoxicated, and he sometimes utters words that are exceedingly sweet. Endued with appalling fierceness, he sometimes laughs loudly, frightening all creatures with his eyes. He sometimes sleeps and sometimes remains awake and sometimes yawns as he pleases. He sometimes recites sacred Mantras and sometimes becomes the deity of those Mantras which are recited. He sometimes performs penances and sometimes becomes the deity for whose adoration those penances are undergone. He sometimes makes gifts and sometimes receives those gifts; sometimes disposes himself in Yoga and sometimes becomes the object of the Yoga contemplation of others.
One specific moment about laughing of Lord Shiva is recorded in Varaha Purana during the manifestation of Lord Ganesha as discussed in this answer: and this answer:
The gods said:
"O great god with three eyes and trident in hand, it behoves you to create (a being) for obstructing the actions of the bad".
Thus requested by Devas, Rudra with great pleasure looked at Uma for a moment.
When he was looking at Uma in the presence of gods, he was worried why no form of his was seen in the sky.
"There is the body in earth, there is one in water; so also in fire and air.
How is it not there in sky ?" So thinking he laughed. By the power of knowledge, by what was seen by Rudra in the sky, by what was said by Brahma formerly as the body of all beings, by the laughter of Rudra, by all these four in the four elements Earth and the rest, there arose a boy effulgent with glowing face, looking like Rudra himself and stupefying Devas with the charm of his dazzling brilliance. Seeing the person of this great boy, Uma remained with eyes stuck on him.
About the types of bodies above mentioned they come under Ashtamurti forms. There might be other instances when Lord Shiva laughed and something new event created that time, I'll update the answer if I find it.
