General loud laughter:
* Roar
* Chortle
* Guffaw
* Howl
* Chuckle (can be loud or soft, but often implies amusement)
More specific descriptions:
* Cackle (often associated with a harsh, unpleasant sound)
* Snort (a sharp, explosive laugh)
* Giggle (a high-pitched, bubbly laugh)
* Belly laugh (a deep, full-bodied laugh that involves the stomach)
The best word to use will depend on the context and the specific type of laughter you want to describe.