Infect deals damage as -1/-1 counters, which can be used to get rid of indestructible creatures. Also, deathtouch can get rid of them, as well.
The only ways to deal with indestructible cards are to counter (eg: Mana Leak ), exile (Path to Exile ), sacrificed by their owners (Dispense Justice ) and through -1/-1 counters (infect, card:Black Sun's Zenith etc).
Deathtouch does not affect indestructible creatures, since it is a "destroy" effect. Indestructibles are immune to it.
Tezz has the right answer, though.
And by the way Indestructible means it's immune to lethal damage and all effects that would destroy the card. So forget Deathtouch.
According to the Comprehensive Rules
702.2c. A creature that's been dealt damage by a source with deathtouch since the last time state-based actions were checked is destroyed as a state-based action.
If a permanent is indestructible, rules and effects can't destroy it. Such permanents are not destroyed by lethal damage, and they ignore the lethal-damage state-based effect (see rule 420.5c). Rules or effects may cause an indestructible permanent to be sacrificed, put into a graveyard, or removed from the game.
It's annoying for sure but not unbeatable by any means.
Doesn't remove the indestructible ability, but it does provide a method of evasion for indestructible creatures, provided the other methods mentioned are ineffective or unavailable.
Here's an interesting tidbit that just came up yesterday: Damage doesn't slough off an indestructible creature, they just get to ignore its effects.
So if you're facing that white knight deck, and they have two Mirran Crusader s and a Knight Exemplar out there, and you cast Slagstorm , you'll deal 3 damage to each creature. ALL THREE creatures get 3 damage marked on them, which stays there until end of turn.
The Exemplar dies to this, since she doesn't make herself invincible. As soon as she does, the other knights lose their indestructibility, and the next time state-based actions are checked, THEY die, because that 3 damage marked on them earlier is still there!