An important point for both the one-time pad as well as other (synchronous) stream ciphers is: don't reuse your key stream.
For the one-time pad, the key stream is the key itself, so this means: don't use a key twice. The two-times-pad is broken.
For OFB and other stream ciphers with an initialization vector (IV), the key stream is decided by both key and IV, which means "Don't reuse a key-IV combination twice". For stream ciphers without an initialization vector, it means: Don't use a key twice.
Reusing a key (or key-IV combination) in stream ciphers is often more fatal than non-streamcipher modes of block ciphers, since we have the XOR-property:
$$ C \oplus C' = P \oplus P' $$
(See more details on how to use this in the question Taking advantage of one-time pad key reuse?)