AFAIK, Curse status is inflicted in a physical attack by like one monster... and a small handful of enemies inflict it with some sort of curse attack (Slap, Curse).
The only attack that even remotely inflicts a multitude of statuses is Bad Breath from the Marlboro... but that's limited to 6 status changes (small, piggy, toad, charm, mute, and darkness)... 3 (4 if you factor in charm) of which prevent you from using the Heal/Esuna spell in battle.