flatulate (formal word)
Verbs unless otherwise noted.
Children's words (kids only!):
make a stink, cut the cheese (sometimes adults use this one)
At the school pageant, Mark cut the cheese so many times that Simon wished he had taken the front of the cow costume.
Polite terms (euphemisms):
pass gas, break wind, toot, S.B.D. (Silent but deadly--a specific subgenre of fart)
Polite people never pass gas. They just clear their throats a lot.
Beans, beans, the musical fruit; The more you eat, the more you toot!
fart (still considered impolite by many people)
cut one, backfire, let one rip
It was an embarrassing day at the emergency room after curious Sandy let one rip onto a lighted match.