Decanting wines, especially reds, really does make a difference. Swirling the wine in the glass brings more air to the wine as well, and this helps release the wine’s lovely and living aromas. Here is a useful article called “The Lost Art of Decanting.”
We decant many of our reds, but only occasionally a white. We find that the whites are more delicate, and often we prefer to keep the wine refrigerated between pours. The bottle with its cork or screwcap goes into the fridge and stays cool but doesn’t pick up any of the other aromas there, whereas putting the decanter into the fridge would be an invitation to a little bit of contamination.
We also use an aerating pourer for all of our reds. It’s a simple one, just a spout. (Many pourers on the market have baffles and all kinds of parts, but those are really hard to clean. Keep It Simple, Slick.) Pourers cost around $10 and they are well worth it.