For many wines, that's a very healthy choice. Most importantly, the oxygen brings out the wine's flavors. Your wine has been closed up, sometimes for years, and it's just kicking to get out and put its best foot, or flavors, forward. There's another reason, too. In red wines, after a few years a sediment begins to form and proper aeration separates the wine from any residue that has built up.
Ports are in a class by themselves and can benefit by several hours of decanting.
Decanting is particularly good for young and tannic red wines. Cabernet Sauvignon, most Zinfandels, Bordeaux, Rhone Valley wines and many Italian wines fall into this category. Tannin is a substance found in wine skins and as red wines are fermented in their skins, a slight bitterness can cling to the palate upon tasting. Aeration softens the tannins and improves the overall taste considerably. The rule of thumb is usually an hour.