Repeatedly using same key on different plaintexts Symmetric encryption:  Does using the same key over and over again introduce a vulnerability?

Meaning, if I transmit a different piece of plaintext encrypted with the same key every day, will an attacker eventually be able to deduce the key?  (In what lengths of time?)
It depends greatly on what form and mode of encryption you use.

For any stream cipher or a block cipher used in a psuedo-stream mode such as CTR or GCM then reusing a key/IV pair even once is absolutely fatal. Never, ever use a static key with them, and if you do, never, ever reuse an IV. They are strictly for one time use keys negotiated via a key exchange algorithm for a particular session.

For modes such as CBC key reuse isn't a big issue even if you accidentally use the same IV again. Re-using the same key/IV will let an attacker determine whether two messages have a common prefix, but won't inherently leak information leading to a breach of the key or plaintext.

So, if you are using temporary keys AND trust your random number generator to be secure and strong then the advantages of CTR or stream mode are compelling especially if speed/parallelization is a concern. If either of these are not the case, such as a pre-shared key or there is no good entropy source, or you don't benefit from the stream cipher characteristics then something like CBC is the way to go.