General Laughter:
* chuckle
* giggle
* snicker
* guffaw
* roar
* cackle
* chortle
* titter
* smile
* grin
Specific Types of Laughter:
* Nervous Laughter: twitch, fidget, smirk
* Condescending Laughter: snort, sneer
* Sarcastic Laughter: scoff, jeer, mock
* Joyful Laughter: rejoice, exult, delight
The best word to use depends on the context and the specific type of laughter you want to describe.