For a fire:
* Extinguish
* Quench
* Put out (the phrase itself can be used as a verb)
* Smother
* Douse
For a light:
* Turn off
* Switch off
* Extinguish
For a cigarette:
* Put out
* Extinguish
* Stamp out
For rumors or information:
* Suppress
* Quell
* Dispel
* Debunk
For a product or service:
* Discontinue
* Cease
* Stop
* Terminate
For a feeling or emotion:
* Suppress
* Control
* Contain
* Subdue
To choose the best verb, consider the context and what "it" refers to.