I now decant most all reds, especially anything with more than a little age, not only to allow the wine to open but to remove the sediment that IMHO can ruin the last third of some bottles.
Most young wines also benefit from decanting, although you don't need to be careful about sediment in young wines. Several years ago my wife and I had dinner at The French Laundry in Napa, and ordered a young Dominus cab. I was surprised when the sommelier pulled the cork and literally dumped the wine into the decanter, as hard and fast as he could. He noticed my look of shock and explained that it was necessary to aerate such young, strong, tannic wine. I've come to believe he was right.
When serving older reds, I use a nice decanter for company or for special occasions, but usually I simply carefully pour the wine into a 4-cup Pyrex measuring cup, using a small flashlight to "candle" it (i.e., to see when the sediment starts to appear). I then pour the last ounce or so into my glass through a coffee filter or a plain white paper towel (which actually does a better job), and have that for myself. I then rinse the bottle with filtered water and pour the wine back into it (known as double decanting) and let it rest until serving time.
Does it help? Most definitely, in my experience anyway. As someone else said, I've never had a bottle go bad after decanting. OTOH, I rarely decant more than 30 minutes before dinner.
BTW, the idea of "letting the wine breathe" by simply pulling the cork and letting it sit on the table is truly the sign of a newbie -- it does next to nothing.