I have some bitcoins on Mt.Gox. Against the possibility that a nuclear holocaust or some sort of hanky-panky or the like were to wipe out Mt.Gox tomorrow morning, how should I back those up?
Mt. Gox operates a hosted (shared) EWallet. They claim to have cold storage and perform other backup practices, but there is nothing that you as a Mt. Gox accountholder can do to "back up" those funds. And if there is a problem restricting you from accessing your Mt. Gox account, there is nothing you can do to recover those funds.
If you have your own wallet, perhaps running the Bitcoin.org client, you then do have the ability (and responsibility) to back it up.
Don't trust MtGox or any exchange to store your BTC. Any BTC on an exchange is at risk of being lost, stolen, or made inaccessible.
So keep your BTC stash in your own cold storage. To do this create a wallet using blockchain.info (or equivalent), create your own BTC deposit addresses and move your BTC from MtGox to your addresses. Now if you keep the associated private keys for your addresses offline, this is what's known as "cold storage". Note that it's actually "warm storage" since your BTC still exist on the blockchain; there is no such thing as real cold storage for BTC. Now you can (and should) back up your private keys.
Your BTC addresses can be added to your wallet as "watch only" addresses (the private key is not required). This way your wallet will be able to display your BTC balance but your BTC is still safe.
To spend your cold stored BTC, import one or more of your BTC addresses into your wallet by providing your private key. The BTC address(es) that you import are at risk, so do not re-use them.