Obviously casting the spell Fire Breath would provoke an attack of opportunity, but would a wizard incur the attacks of opportunity while using the breath weapon? I ask because I know the alchemist's Breath Weapon Bomb discovery does not provoke attacks of opportunity when used.
It would not provoke unless it is also a ranged touch attack. That is the only time that use of a spell provides a 2nd potential AoO unless the spell specifically says otherwise.