How long can an opened bottle sit with a cork before spoiling? I'm assuming that oxidation will takes its toll. And should red wine breath?
Oxidation happens pretty quickly with wine. You can buy vacuum sealers that work with a pump and will preserve the wine a little longer. That and keeping it in the fridge over night. A day or two is probably the max you would want to keep a wine, but as in all things YMMV. Left open, it won't spoil, per se, but the flavors will degrade.
Not all red wine needs to breath. Older wines need it more. As you noted, wine will change as it breathes. Bigger wines (cabernet, heavy reds) tend to change more, as there's more complexity.
As noted above, I can't speak much to white wines...