I get asked this a lot, and quite frankly the answer is tricky. According to Kevin Zraly, author/teacher/wine badass, only 4% of wine is meant to be drunk more than 1 year after its release, and only 1% can improve with more than 4 years age. That means, in it's most simple form, drink most of your wine now, and don't worry too much about it. Not a helpful answer, I know.
If you are looking to age wine, you must first determine what your goals are. Let's surmise that you have the wines that you want to drink in the next year or two taken care of, and you want to know what will age more than that. This depends heavily on the producer, the grape, and the vintage that the wine comes from. Some of your safest bets for really long term wines are ports, madeira, and sherry. The producers have already beat the tar out of these wines, and they will last indefinitely. I have drank madeira from 1898, and it was wonderful. Next, look mainly to Europe. This is because they usually build their wines to last a bit longer over there. I would loook into high quality Burgundy, Bordeaux, Chateauneuf-du-Pape, Chianti, and Barolo if you want wines that will run the course. You do, however, have to look into the vintage. For example, 2003 was really hot in France. This means that the grapes were a lot riper and had more sugar at harvest. As a result, the wines are bigger, fleshier, and will drink better in their youth. Compare this to the 2005 which was a bit cooler year, and the wines will last a lot longer in your basement.
Other wines from across the pond that will do well with age are quality German/Alsacian Riesling (nothing in a blue bottle- drink that stuff yesterday), and some from the Loire (Coulee de Serrant, Quarts du Chaume). Many spanish reds, particularly from Rioja and the Ribera del Duero will go nicely for 10 years or so.
Finally, don't count California out. Some of these producers are finally pulling in the reins on their wines, and making cabs and pinots that will go a long time. As Americans, we tend to pop the cork on the newest releases way too early. It's okay, let that Pride Cab go for a few years, you will be amazed by the difference. If you still have some doubt, the best way to tell if a wine will age is to buy 3 or 4 bottles of it. Drink one now, one in a year, and one in 5 years. If you are keeping good notes, you will really see how the wine progresses. Sometimes you will be right, sometimes a wine will surprise you - and that's part of the fun!
Today is the day to go out and buy a bottle of port for the cold weather. Go find yourself a 10-year tawny from Taylor Fladgate, Dows, or Gould Campbell. Drink a small dram tonight with the wind and rain, and save the rest to sip on over the next few weeks. Delicious.