Wine's worst enemy is oxygen, which bruises the liquid much the same way that air causes the flesh of a peeled apple to spoil and turn brown. After a day or two, most opened wines will begin to degrade significantly in flavour. After three or four days, most will taste unpleasant, losing their freshness. The spoilage reactions that harm wine slow down as temperature drops. That's why freezing works. It's a good way to stop those reactions cold. Wine freezes at roughly -8 to -10 degrees Celsius, depending on the alcohol content (the higher the alcohol, the lower the freezing point).
Many people have conducted blind tastings of previously frozen wine and found them to taste better (after weeks or even a month) than opened wines preserved using other methods. One common and reliable method is to inject the air cavity of the bottle with an inert gas, such as argon. You can find spray bottles of such gases in wine shops; a popular one is called Private Preserve.
The key when defrosting a wine is to give the half-empty bottle a swirl before pouring. Alcohol and other components in a wine can separate away from the water as it freezes. Swirling will help it to re-mingle those components with the water.
That said, I wouldn't use the freezing technique on very expensive bottes. Most very fine red wine in particular is bottled unfiltered. This implies that the wine will contain more flavour-imparting solids from the grapes. Those tasty solids could precipitate out of solution as it freezes and may not re-integrated with the fluid even if you stir it up.
And remember that this all pertains to opened bottles of wine. Freezing a full, sealed bottle is a no-no. Wine is mostly water, and water expands as it freezes, usually so much so that it will push out the cork and make a bit of a mess in your freezer. Worse, it could crack the bottle, especially in the case of sparkling wine, whose corks are typically sealed tight with a wire cage. Sparkling wines produce a lot of pressure and could explode.
If you don't want to go the freezer route, simply store your wine in the fridge. Even fridge temperatures will significantly slow down the degredation. I always store my half-opened wines in the fridge, even when i'm using argon gas to keep out the oxygen from the air cavity above the fluid.