Atomic cross-chain trading Atomic cross-chain trading describes a method where two parties, owning different crypto currencies, can safely exchange the crypto currencies without an intermediary. The method is described in the link below: 

https://en.bitcoin.it/wiki/Atomic_cross-chain_trading

Are these method of exchange already possible with Bitcoin and popular alt-coins like Litecoin/Dogecoin? Or is it still a work in progress that requires changes to the core code? If atmoic cross chain trading is possible, are there any transactions in the blockchain where atomic cross chain trading has been used?
To exchange between Bitcoin and popular alt-coins like Litecoin/Dogecoin you will need to use the first solution ('using revealing secrets of contract'). 

The second solution is designed around a hypothetical custom altcoin which is designed specifically to support the described exchange algorithm. I don't think that such an altcoin actually exists, but there definitely isn't support for this in Litecoin or Dogecoin.

There is a problem with the refund transactions in the first solution, however, with the current Bitcoin version, due to transaction malleability.

The problem is that refund transactions need to be signed before submitting base transactions to the blockchain, but the base transactions can potentially be mutated before they get to the blockchain, which would invalidate the refund transactions and prevent coin being reclaimed in the event of aborted exchange.

I discuss this issue in some more detail in this blog post, where I also look at a generalised form of the 'pay on reveal secret' transaction semantics in this exchange algorithm, and discuss other ways in which this can be implemented.

Note that it's possible to make this work in an embedded protocol, and then perform trustless exchange between blockchains with the embedded value tokens as intermediary steps. I've made a working version of this setup in the form of SwapBill, and this is set up and can be used, currently, for trustless exchange between testnet Bitcoin and testnet Litcoin.


  If atmoic cross chain trading is possible, are there any transactions in the blockchain where atomic cross chain trading has been used? 


There are definitely SwapBill atomic exchange transactions on the Bitcoin and Litecoin testnet blockchains, but this is not really what you are asking. ;)