General Synonyms:
* Stop
* End
* Halt
* Terminate
* Discontinue
* Finish
* Quit
* Suspend
* Abolish (for something permanent)
More Specific Synonyms:
* Desist: to stop doing something
* Refrain: to avoid doing something
* Abstain: to refrain from doing something, especially something enjoyable
* Withdraw: to stop being involved in something
* Give up: to stop trying
* Come to an end: to finish
* Expire: to come to an end, usually referring to a time period
* Fade out: to gradually decrease in intensity or importance
Figurative Synonyms:
* Die down: to gradually decrease in intensity
* Wane: to decrease in strength or importance
* Pass away: to die (used for a person)
The best synonym for "cease" will depend on the specific situation and the desired tone.