I think most clients now let you export your private keys so that you are not 'locked in' to a particular client.
Generally the easiest and safest way of moving bitcoin from one client to another is to simply send the bitcoin with a normal transaction rather than moving private keys around. It is very easy to get confused with having multiple copies of the same private keys in multiple clients. For instance change addresses are worked out differently in different clients so it gets hard to see what is going on.
In some rare instances you do want to stop using one client and move your private keys to another. For instance you may be unhappy with the client you are using or it is unavailable for some reason. For MultiBit I have written up how to do this between MultiBit and blockchain.info in the help. It's here:
https://multibit.org/en/help/v0.5/help_movingAWallet.html(Actually because of a change in the blockchain.info wallet format moving from blockchain.info to MultiBit is currently not working - it'll be fixed in the next version of MultiBit).
I would say 99% of the time the safest option is to leave your private keys in one client (but make sure you have backups of the wallet/private keys just in case).
