Excerpted fragment from the Dictionary of Expressions of Amusement, Joy, and Delight:
Cackle
Wicked, loud, nefarious, uncontrollable, harsh.
Cachinnate
Unused, unclear, ugly and only found deep inside a thesaurus. People don’t use this one.
Chortle
Who chortles anymore? The chortle is extinct (possibly endangered). Theorists and reconstructions alternatively posit and model the chortle as a nasalized guffaw.
Chuckle
A light, forced laugh that accompanies the telling of a bad joke. This is fleeting, brief or ephemeral but never all three.
Crack up
Hysterical laughter, possibly under an influence but not necessarily.
Guffaw
Glottal, guttural a giggle at the back of the throat; when you hear this laugh you laugh at not with. A more evolved chortle that comes from a place deeper inside.
Giggle
Childish, cute, high pitched. Forty-year-old opera singers do not laugh like this.
Howl
A single, protracted note that may waver slightly, typically followed by a cackle or a lengthy beat poem.
Laugh
“Ha ha ha,” (alt. sp. “hahahah”), “hee hee hee,” (alt. sp. “heheheh”) Ho Ho Ho, Hu hu hu. Hi hi hi is just exceedingly happy to see you. And sometimes Y is but in this case it isn’t.
Scoff
This laugh emanates from a bourgeois representative of white male western euro-centric paternalistic patriarchal hegemonic repressive capitalist society.
Snicker
Sinister, slippery, slimy and nasal. Some accuse the snicker as the predator who doomed the chortle because like all things evil it is slightly tainted by a twanging from the nose. There is no conclusive evidence the snicker is responsible for the loss of the chortle.
Snigger
For people who would snicker but have a cold or a permanently damaged nasal cavity.
Squeal
Oinkish, porcine, and pink, Jewish people do not squeal because it is not kosher and muslims do not squeal because it is had (a violation Islamic law). Wasps might squeal but they are insects and do not laugh.
Titter
A fronto-labial laugh that escapes through rapid-fire friction with the foremost front teeth. This laugh is a characteristic of mischievous female youth.
Twitter
Like a titter but with a slight lisp.