Can I "clone" my credit card using the Nexus S and Galaxy Nexus's NFC chip? If not, why not? Can an android app read my credit card's NFC data, store it and then send this data to a contactless pay point (PayPass)?  Thus I would use my Nexus to pay for my coffee, conveniently.

If yes, is there an app for this? If not, why not?
No, you can't. To oversimplify - wireless payments (NFC, RFID chips on cards, etc) aren't a simple 'what's your card number' transaction (because that would be insecure beyond belief), they are more of a 'here, encrypt this block of data with your secret numbers and return it' type of thing. 

The block of data to be encrypted changes for each transaction, and there's (supposed to be) no way to get the device to spit out it's secret numbers.

So you can't EASILY clone your cards onto your phone (if you could, then so could anyone else who walked near you).

That's not to say it can't be done at all (if, perhaps, you found a flaw in the way the crypto works, you could perhaps deduce the secret numbers of a device), but it's not something you're going be buying an app for.