The likelihood of breaking, for instance, an AES-128 cipher is 100% after $2^{128}$ tries in brute force, meaning that I've got to try $2^{128}$ keys to certainly break it.
What if I (hypothetically) had recorded $2^{128}$ bits of data encrypted with the same AES-128 key? How does this help in cryptoanalysis?
And how is the situation differently if or if not a part of this data (e.g. word file headers, specific telnet handshakes, whatever) was known plaintext?