General Negation:
* No
* Never
* None
* Neither
* Without
* Lacking
* Absent
* Empty (for lack of something)
Formal Negation:
* Negation
* Denial
* Refutation
* Contradiction
Informal Negation:
* Nope
* Nah
* Ain't (informal, avoid in formal writing)
Specific Contexts:
* Don't (for verbs)
* Can't (for ability)
* Shouldn't (for obligation)
* Didn't (for past tense)
The best synonym for "not" will depend on the specific sentence and the desired tone.