Indestructible

Indestructible was an attribute that some permanents have and becomes a keyword in Magic 2014. Indestructible permanents can't be destroyed by rules or effects. Indestructible permanents can still be put into their owner's graveyard by other means, such as by the "legend rule", by being sacrificed, or in the case of creatures having zero toughness.

The first card that conferred indestructibility was Consecrate Land in Alpha followed by Guardian Beast in Arabian Nights, but no other cards followed (and no formal rules existed) until Darksteel.

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Rulings

Damage accumulates on indestructible creatures, and that damage is removed during the cleanup step.
Lethal damage is defined as an amount of damage greater than or equal to a creature’s toughness. Even though an indestructible creature isn't destroyed by lethal damage, that definition is still used for things like assigning trample damage.
If a creature with lethal damage on it stops being indestructible, it's destroyed the next time state-based effects are checked.
Being indestructible stops only effects that would destroy the permanent, including destruction due to lethal damage and destruction that doesn't allow regeneration. An indestructible permanent can be exiled, returned to a player's hand, put into a graveyard for having 0 or less toughness, or sacrificed.
You can use a regeneration effect on an indestructible permanent, but since that permanent can't be destroyed, the effect does not apply, unless it loses indestructibility before the end of the end step, then it would regenerate.

Magic 2014 updates:

In most cases, indestructible becoming a keyword doesn’t represent a functional change. There are two exceptions:
Previously, if a permanent was made indestructible by a resolving spell or ability (such as Withstand Death), and then that permanent lost its abilities, it would still be indestructible. This was because indestructible wasn’t an ability; it was just something true about the permanent. Now, the permanent will gain the ability indestructible, and it will lose this ability along with its other abilities.
Previously, if a group of permanents were made indestructible by a resolving spell or ability (such as creatures you control being affected by Rootborn Defenses), permanents that joined that group or entered the battlefield after that spell or ability resolved would also be indestructible. This was because the effect making the permanents indestructible wasn’t changing any of those permanents’ characteristics. Now, a permanent that enters the battlefield or comes under your control after the spell or ability resolves won’t have indestructible as it wasn’t under your control at the appropriate time to gain it.