What methods are currently used to embed additional data into the Bitcoin blockchain? Yes, I do understand that it is inappropriate to pollute the already large blockchain with data not necessary to make the currency work. But I know people are using Bitcoin as an underlying system for certain applications, like data storage or reaching common consensus about matters not directly related to the currency itself.

What methods are mostly employed to inject the blockchain with arbitrary data (like custom scripts representing data or payouts to addresses that represent data)? Is there a need to stop this in order to prevent an undownloadable large blockchain from forming in the future? If so, how can this be accomplished?
The accepted method of doing this is by putting the data in the output script along with op code OP_RETURN which tells clients to mark the transaction as invalid. This way, it doesn't use up as much resources on clients who don't care about non-transaction related data. 

There are two schools of thought regarding putting arbitrary data in the blockchain. Some believe that as long as the method used to put arbitrary data in the blockchain follows all the rules of the bitcoin protocol, there is no harm done and that it actually strengthens the network by increasing usage. Others believe that it is detrimental and that these kinds of data should be kept from using up resources on a network that is designed to process transactions and not designed to store arbitrary data.  

In my opinion, it all really comes down to what miners think about these kinds of use of the blockchain and from their perspective , they really don't care. To a miner, it makes no difference what the transaction is as long as it pays a transaction fee ,and they can add it to their block. So I believe that this kind of usage of the blockchain is here to stay.