Does a creature with indestructible survive being dealt damage equal to its toughness?

Normally, a creature is destroyed when it has damage marked on it equal to or greater than its toughness (CR 704.5g). However, indestructible is a static ability that explicitly prevents a permanent from being destroyed (CR 702.12b). Since the damage-based state-based action destroys the creature, and indestructible prevents destruction, the creature survives.

It is important to understand that the damage is still marked on the creature — it does not vanish. The creature simply cannot be destroyed by that damage. Other effects that cause the creature to die without using the word 'destroy' (such as reducing its toughness to zero or below via -1/-1 counters or toughness-reducing effects) will still kill it, because those trigger a different state-based action (CR 704.5f) that is not destruction.

Indestructible also protects against explicit 'destroy' effects, such as removal spells that say 'destroy target creature.' The creature will simply remain on the battlefield regardless.

Example: Your 2/2 creature with indestructible blocks an opponent's 5/5. The 5/5 deals 5 damage to your creature. State-based actions check: 5 damage ≥ 2 toughness, which would normally destroy it, but indestructible prevents that destruction. Your 2/2 stays on the battlefield with 5 damage marked on it.

Note: if something like a spell reduces your indestructible creature's toughness to 0 (e.g., via -X/-X), it will be put into the graveyard due to CR 704.5f, which is not destruction — so indestructible does not save it in that case.