Does a spell that says destroy all creatures also destroy creatures with regeneration if they don't regenerate in response?

Regeneration is a replacement effect that substitutes for destruction — but it only works if the regeneration ability is activated (or triggered) and resolves before the creature would be destroyed. If the controller of a creature with regeneration chooses not to activate the ability, or simply lets the spell resolve without doing so, the creature is destroyed just like any other.

According to CR 701.15a, to regenerate a creature means to replace the next time it would be destroyed with a different set of effects (tap it, remove it from combat, remove damage from it). This replacement only applies if a regeneration shield has actually been set up before destruction occurs.

When a spell like Wrath of God resolves, it destroys all creatures simultaneously (CR 509.2 covers the destroy step in combat, and the same destruction process applies to spells). Any creature that did not have a regeneration shield in place at that moment is destroyed. Regeneration does not automatically trigger — the ability must be explicitly activated (usually by paying a cost) before the destruction event.

Example: You cast Wrath of God. Your opponent controls a Troll Wurm (which has regeneration). If your opponent does not pay the mana cost to activate its regeneration ability before Wrath of God resolves, Troll Wurm is destroyed and goes to the graveyard just like every other creature on the battlefield.

So the key condition is: regeneration only saves a creature if its controller proactively activates (or otherwise creates) a regeneration shield in response to the spell, before the destruction event actually happens (CR 701.15a, 614.1).