When is a cipher considered broken? We've all read how some people claim AES is broken because there was supposedly a way to get the plain text from a cipher text faster than brute-force. But is this the definition?

Is a cipher broken if you can get the key faster than brute-force? Or is there another definition for "broken"? Because if you have a 128-bit key and it takes $2^{126.5}$ operations to break it, I wouldn't call that broken, for that I find broken a bit of a strong word.

I did find this for an asymmetric key and the quote:


  An asymmetric authentication scheme is considered to be broken if an attacker with access to the verification key can generate any valid cipher text, even if he can convince you to sign arbitrary other plain texts.


...which isn't really applicable to symmetric keys. It is a perfect answer for asymmetric encryption but I'm looking for something more general or I could make a distinction between symmetric and asymmetric but then I would still like to know, when is a symmetric encryption scheme deemed broken?
Your explanation is "broken in the academically sense" - there is a theoretical way to break the algorithm better than brute force. AES is broken in this way. There's also "broken in the practical sense", which means you can break an cipher in real applications or protocols. AES is still safe in this sense, because you still need too much computation power and even related keys to get the original key.

There are also different attack scenarios. You can have ciphertext-only attacks - the attacker only knows the ciphertext. That's a pretty weak attack scenario and not realistic. What if the attacker knows some of the encrypted plaintext because it has a pattern? That's the known-plaintext attack. There are some more kinds of attacks with even more help for the attacker, but they are harder to do in the real world, but even if an algorithm is broken with one of this harder threats, that doesn't mean that the algorithm can't be used anymore. AES is secure because the attacks still need too much work to get the key.