Whether the bottle has been opened or not, the short answer is: Not very long.
Let's start with a never-opened bottle of wine. The problem with your kitchen fridge is that, unlike Betty Draper's fridge on Mad Men (which had to be defrosted regularly back in the 1960s), today's models are frost-free, which means they're constantly dehumidifying the contents. So, wine stored in your fridge is at risk because the cork is being sucked dry, slowly, every day. Now, I know what you're thinking: I wish I could wake up in that fridge every morning! But you can't. And your wine shouldn't either, or at least not for more than a couple of weeks. Best to store your wines in the coolest, darkest part of your house or apartment, and then chill them only once you're ready to drink them.
So, what about that bottle of wine you didn't quite finish last night? Store it in the fridge for exactly one night, and no more than that. Air in the bottle is, generally, a bad thing, so once you pull the cork the clock starts ticking. Put the cork back in the bottle, put it in the fridge, and let the air trapped in the bottle do some good: It'll help open the wine up a bit more—but hopefully not too much. You'll never know until you taste it the next day...
—Follow Anthony Giglio on Twitter at @WineWiseGuy.