Formal:
* Rire aux éclats: This is the most literal translation and means "to laugh in bursts."
* Rire à gorge déployée: This translates to "to laugh with open throat" and conveys a sense of unrestrained laughter.
Informal:
* Éclater de rire: This means "to burst into laughter" and is a common way to express a sudden and loud laugh.
* Se tordre de rire: This translates to "to twist with laughter" and implies a very intense and enjoyable laugh.
* Rire comme un fou: This literally means "to laugh like a madman" and is a more exaggerated way of saying "laugh out loud."
Slang:
* Péter un câble: This is a slang term that means "to blow a fuse" and is used when someone laughs uncontrollably.
The best option for you will depend on the specific situation and your desired level of formality.