Is the one-time-pad a secure system according to modern definitions? Occasionally I hear people say that one-time pads are "useless" or even "broken".


  "modern cryptography knows more security definitions, under some of
  which the one-time pad is completely broken."
  -- How do we know a cryptographic primitive won&#39;t fail suddenly?


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  One time pad: why is it useless in practice?


...


  "we don’t need (and shouldn’t want) to use one-time pads"


...


  "The one-time pad is not a semantically secure encryption
  algorithm."


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  "One-time pads may be theoretically secure, but they are not secure in
  a practical sense."
  -- Bruce Schneier


What specifically are these "modern ... security definitions", and how exactly is the one-time pad completely broken?
Modern security has moved beyond looking just at passive attacks (in which the attacker is just a passive eavesdropper seeking to learn what was said); attackers are generally considered to be able and willing to pull off active attacks of various types (in which the attacker can modify or forge messages to achieve some goal). One-time pads are extremely vulnerable to modification; if an attacker knows that a message says "Pay Robert \$100,000", they can trivially change it to "Pay Joseph \$999,999". They share this property with all stream ciphers; if your ciphertext is the plaintext XOR a keystream, then an attacker who knows $P_1$ and $C_1$ can easily compute $C_2=C_1\oplus (P_1\oplus P_2)$, which decrypts to $P_2$. Working around that requires some way to verify message authenticity, which a one-time pad doesn't do (and doesn't try to do). This is provided by message authentication codes (MACs), or by a cryptosystem that combines authentication and encryption (like AES-GCM).

Also, many security properties literally do not apply to OTPs, because the properties are along the lines of "given the ability to encrypt multiple messages with the key, do X." 

Uselessness is broader: even if you just need confidentiality, OTPs have serious issues for usability. That's because a OTP key has to be as long as the message and transmitted in secret; cryptography is most useful when you just need to transmit a little information secretly to encrypt a lot of stuff. An OTP is only as secure as the key exchange, so to be useful the keys have to be exchanged without relying on cryptography for security (else you're not getting perfect security). There are a few cases where they work well (like distributing in person to someone who's about to go on a mission and will need to send stuff back to you over an insecure channel), but they're rare.