General:
* Talking rapidly
* Babbling
* Gabbing
* Prating
* Gossiping
* Jabbering
* Blathering
* Spouting
* Gushing
More specific:
* When referring to teeth: Clicking, clattering, gnashing
* When referring to birds: Chirping, twittering, trilling
* When referring to machines: Clicking, rattling, whirring
Figurative:
* Buzzing
* Humming
* Whispering
* Murmuring
The best synonym will depend on the specific situation and the tone you want to convey.