Some red wines benefit from being allowed to breathe for some time before being drunk. If I'm using such a wine for cooking rather than drinking, do I still need to let it breathe?
Not really. Letting the wine breath is basically just allowing some of the phenolic components of the wine oxidize lightly, which can improve the wine in your mouth. However when you are cooking, you are beating the piss out of the wine anyway and loosing most of the gentler esters that are improved thusly. Additionally the wine is breathing plenty in the skillet.