A battle with indestructible still loses defense counters as it's dealt damage. If it's a Siege, it will still be exiled when the last defense counter is removed from it, and its controller may still cast it transformed without paying its mana cost.

Because damage remains marked on a creature until the damage is removed as the turn ends, nonlethal damage dealt to a creature you control may become lethal if Avacyn leaves the battlefield during that turn.

A planeswalker with indestructible still loses loyalty as it's dealt damage. It is put into its owner's graveyard if its loyalty becomes 0.