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Any creature whose toughness is reduced to 0 or less is put into a graveyard as a state-based action, regardless of whether or not it is indestructible. You could use creatures with wither or infect or you could use spells like card:Black Sun's Zenith and Disfigure to reduce the toughness of the indestructible creatures until they die.
1.) Exile it
2.) Make you opponent sacrifice it
3.) Minus counters
4.) Pacifism or any other cards like it
5.) Depending on what colour it is, if you have a creature which has protection from what ever the indistructable creature is then no damage can be dealth by the indestructable creature to the protected creature.
6.) Return it to their hand
7.) Counter it before it comes in
These can all stop them from bothering you.
Actually the accepted answer is incorrect based on the game rules. Lethal damage does not destroy, or 'kill', a creature with indestructible. Please refer to rule 700.4 as I have pasted below:"700.4. If a permanent is indestructible, rules and effects cant destroy it. (See rule 701.6, Destroy.) Such permanents are not destroyed by lethal damage, and they ignore the lethal-damage state-based action (see rule 704.5g). Rules or effects may cause an indestructible permanent to be sacrificed, put into a graveyard, or exiled."Therefore the only way to destroy an indestructible is via the other actions other users have posted.
@0610cja: Actually, it is you who is incorrect.
Indestructible simply means this permanent can't be destroyed. That's it. Any other means of killing a creature (reducing its toughness to 0 or less, causing it to be sacrificed) still puts that creature into its owner's graveyard. Neither 0 or less toughness nor sacrifice cause a creature to be destroyed.
I'm curious now. From where did you source your information?
Allow me to clarify my answer. Lethal damage, I.e. from defending will still reduce an indestructibles toughness to zero but since indestructible prevents the creature from going to the graveyard due to lethal damage it is not destroyed, and its toughness returns to its previous level after combat is resolved. Indestructible does not prevent damage, just the effect of that damage. -1 counters are technically not considered damage so therefore if you bring the toughness below zero in this manner, and since no creature may have 0 or less toughness, it is sacrificed as a state based action. No damage was ever done to the indestructible this way. There is a difference and this has led to much confusion and research on my part since a majority of people tend to explain the rules to me in their own words and not exactly how the rules define them. Though who wants to study the game rules, besides myself..
@Skeletontree: Almost every part of that post is incorrect.
Damage does not reduce a creature's toughness unless that damage is dealt in the form of wither or infect.
In the case of wither and infect, -1/-1 counters are considered damage, as that is how a source with wither or infect deals damage to creatures.
Creatures with 0 or less toughness are not sacrificed. They are simply put into their owner's graveyard as a state-based action.
I apologize if I have misquoted something. Here are the points I was trying to outline albeit incorrectly as you have stated: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 creatures 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.