OP_RETURN
OP_RETURN is a script opcode used to mark a transaction output as invalid. Since any outputs with OP_RETURN are provably unspendable, OP_RETURN outputs can be used to burn bitcoins.
Is storing data in the blockchain acceptable?
Many members of the Bitcoin community believe that use of OP_RETURN is irresponsible in part because Bitcoin was intended to provide a record for financial transactions, not a record for arbitrary data. Additionally, it is trivially obvious that the demand for external, massively-replicated data store is essentially infinite. Despite this, OP_RETURN has the advantage of not creating bogus UTXO entries, compared to some other ways of storing data in the blockchain.
From Bitcoin Core release 0.9.0:
This change is not an endorsement of storing data in the blockchain. The OP_RETURN change creates a provably-prunable output, to avoid data storage schemes – some of which were already deployed – that were storing arbitrary data such as images as forever-unspendable TX outputs, bloating bitcoin's UTXO database.
Storing arbitrary data in the blockchain is still a bad idea; it is less costly and far more efficient to store non-currency data elsewhere.
OP_RETURN applications
OP_RETURN can be used for digital asset proof-of-ownership, and has at times been used to convey additional information needed to send transactions (see ECDH address).