You don't need to be a wine snob to notice and be concerned about the effects of oxidation. As a complete wine novice buying my first bottles of wine, I could tell without any training that the flavor of the wine was different the day after it was opened. Several wine preservation products are available that help to minimize the effects of oxidation.
The best household wine preservation system is The Keeper (above left). I use this product with every bottle of wine I open at home. The stopper-faucet that dispenses the wine is connected to a nitrogen cylinder. Nitrogen (an inert, non-oxidizing gas) fills the space inside the bottle as the wine goes out. This device prevents oxygen from coming into the bottle and thus keeps oxidation from occurring.
A widely used but significantly less effective product is Private Preserve inert gas spray (pictured to the right). Each time a bottle of wine is opened or reopened, you are supposed to spray Private Preserve (a combination of nitrogen, carbon dioxide, and argon gas) into the bottle. These gases are allegedly heavier than other gases and are said to lay down a protective blanket over the surface of the wine, keeping oxygen at bay.
I used Private Preserve for years, and it certainly slows down the oxidation process. It is better than nothing and something you might want to consider buying, if you're not ready to spend money on The Keeper. However, it is only marginally effective at preventing oxidation. The money spent on several bottles of Private Preserve would be better spent on The Keeper.
A completely worthless product that is commonly seen in wine shops is the Vacu Vin Vacuum Wine Saver (pictured at left). This was the first wine preservation product I ever tried. A dinky little pump is supposed to extract most of the air inside your bottle of wine, again slowing down the oxidation process. The pump, however, is exceptionally weak and the stopper that goes on top of the bottle does not form a very tight seal. Vacu Vin may remove some oxygen from the inside of a bottle, but it is an almost completely ineffective product. Don't throw away your money on this one.
Ken Shockley laughs at my Keeper wine system every time he comes over to my house. I must admit that it looks rather odd, but it has been a wonderful investment. It can keep opened bottles of wine fresh for weeks, allowing me to enjoy wine at my leisure. I highly recommend it.