How long will my encryption remain private? This is a basic question in cryptography but I have not found a good, comprehensive answer.

It is explained that our keys should expire and we should get new, stronger ones with time, reflecting more powerful decryption computing. Does that mean that emails encrypted today will become easier (even trivial) to decrypt in future, so emails encrypted today will eventually lose today's privacy?

If so, what is the general opinion on how this affects notions of privacy by encryption?
The main good reasons to change keys periodically are:


to mitigate the risk of a key compromise; at least some ways keys get compromised are a one-time event, e.g. eavesdropping of the keyboard protecting the passphrase; changing the key thus restores security until the next leak, and only messages enciphered with the leaked key are compromised (and only those actively intercepted after the leak if the scheme provides forward secrecy)  
so that humans remember the procedure;
addition per comment: in order to reduce the risk coming from using the same key of a block cipher for too many blocks; e.g. for 3DES in CBC mode: if the adversary has 32 GiB of known plaintext (e.g. all-zeroes of an idle link), chances that she can decipher 8 meaningful bytes from another 32 GiB worth of data are >63%.


The main reason to increase key size (which is, or at least should be exceptional compared to key change) is to induce retirement of the obsolete tools used to process the keys; not only is it business to security vendors, it often is the best way to increase security; for examples, if 1024-bit keys are deemed no longer usable, chances are that the Smart Card holding them will be replaced by newer ones, designed with better side-channel leakage protection. In my experience, resistance against brute force is rarely the real weak point in a commercial application (except if that was engineered-in, e.g. to meet some legal requirement).