General Laughter:
* Chuckle: A soft, quiet laugh.
* Giggle: A high-pitched, nervous laugh.
* Snicker: A suppressed, often disrespectful laugh.
* Grin: A broad smile, often accompanied by a chuckle.
* Smile: A facial expression of pleasure, often accompanied by a slight laugh.
* Chortle: A hearty, loud laugh.
* Roar: A deep, booming laugh.
* Guffaw: A loud, boisterous laugh.
Conveying amusement:
* Amuse
* Titter
* Cackle
Conveying derision:
* Scoff
* Mock
Conveying joy:
* Rejoice
* Exult
* Celebrate
The best synonym for "laugh" will depend on the specific situation and the emotion you want to express.