Certain escrow techniques rely on one party being able to "destroy" these bitcoins, without being able to steal them. For example I could put 10 bitcoins in escrow, giving a second person the ability to destroy them. Now if that second party lends me, say, 5 bitcoins, I can't simply run away from my debts without incurring a loss larger then the debt itself, once the other party destroys the bitcoins. There are variations of this scheme for a number of other purposes.
You don't want to actually destroy bitcoins in such a scheme, but you want the threat of destroying them.
But "destroy" in this context isn't necessarily an actual destruction, as long as "destroyed" bitcoins are a loss for both parties. Donations to trusted organizations are an alternative.
1I think this is the wrong answer. There are actually schemes that rely on being able to permanently destroy bitcoins (don't know enough about it to write an answer myself though). – Thilo – 2012-03-20T02:10:03.403