During my opponent's turn, he plays Fumigate to wipe the board. I respond with Repel the Abominable. Do all of our creatures die, or do none die?
Fumigate:
Destroy all creatures. You gain 1 life for each creature destroyed this way.
Repel the Abominable:
Prevent all damage that would be dealt this turn by non-Human sources.
Fumigate does no damage; it destroys. All the creatures die; Repel the Abominable does nothing to stop it. If you wanted to keep your creatures, you'd have to seek another means of preventing their destruction, such as by regenerating your creatures (e.g. Dark Dabbling) or making them indestructible (e.g. Boros Charm). For thoroughness, protection wouldn't work.
Damage can lead to a creature being destroyed, but being destroyed doesn't necessarily have to involve any damage at all.
If it did do damage, it'd say so: Wave of Reckoning and Blasphemous Act are board wipes that deal damage.
