It's frequently stated that EMV cards cannot be cloned. I'd like to know, specially with commodity smart card readers/ writers, why is this true? What specific data cannot be read using commodity hardware, and what type of hardware would be required to do so?
To use an analogy, expanding on what people have said about it being a chip:
An older style magstripe card was simply a string of characters encoded onto the card, it could be read, or written, and that was it. It's like a page of a book, you can read it, but if you don't understand, you can't ask it questions.
An EMV chip is a small microprocessor. It runs a specific application. You can't just read what it knows, but you can 'ask' it 'questions' by issuing commands from the EMV set, and see what it returns. Unlike Magstripe, it's interactive, and is capable of both answering and more importantly, refusing to answer queries.
All of this is a little simplified. Encryption obviously plays a large role in EMV, and it's much complex than just some little microbug that you can interview, like I make it sound, but the essence is there.
Like @Lucas Kauffman has mentioned, EMV isn't unclonable, but it is significantly more difficult, at least if you start from first principles. As with many security issues, these complex differences will start to mean less and less now that vulnerabilities have been found, because it will be possible to buy cloners without needing to know how they actually work.
The chip is actually a device which can perform calculations execute instructions. It's used for challenge response as to authorize attackers. It's therefor not possible to just clone them.
There are attacks against the EMV cards as demonstrated by the University of Camebridge. They published a paper about it named "Chip and Skin: Cloning EMV cards with a preplay attack".
The attack heavily relies on flawed random number generator used by the bank terminals. There is also a Defcon presentation on chip & pin which can be found here.
I attended an OWASP chapter meeting last year where Senior Cambrdige ResearcherSteven Murdoch presented their attack. He also noted that recently criminals had realized to reduce the attack for which they needed a complete PC in a back pack, to a simple chip which can be fit in plastic banking card (the chip itself was a mere 3 mm longer).
The key is that EMV cards don't just output the same response every time. They're a challenge-response system: they work by reading a "challenge" message from the terminal, doing some computation within the chip, and then outputting a unique "response" message back. If you capture that response, you're only capturing one possible output -- the one that corresponds to the challenge it was sent. Since a terminal should never output the same challenge twice and the challenge should be unpredictable, then that capture response should be useless in the future.
In order to fully clone an EMV chip, you need to know the secret that's stored inside it. Since it never transmits that secret, obtaining it is impractical.
This in contrast to other identification technology such as RFID and magnetic stripes which only know how to transmit one number. In the case of these technologies, cloning that output is reasonably simple.