Should wine be stored in or out of the fridge once it's opened?

I know red wine is generally served at room temperature, but after it's been opened should I store it in the fridge, or on the counter? White wine, I'm assuming is stored in the fridge after opening.

For most cases, in the fridge is best for both red and white.

If you like the way the wine tastes, then you want to keep it cold and away from air. I found the best way to do this is to get a 4-pack of blue-fish or other small (187mL) wine with screw caps, and glass bottles. Fill these to the top with your leftover wine, and put in the fridge. Seems to hold flavor profile for a week or so. This also gives you about 1-glass per bottle which can be good for mid-week glass with a meal.

If a red wine is tannic then having some extra air and sitting on the counter at room temp overnight can help to reduce the bitter taste.

Some people freeze wine. Haven't tried that yet, but apparently there has been some good success.

This is a good idea to use left-over bottles. I have freezed wine to use for cooking and it freezes fine, but is slushy. If I have time, I can cook the alcohol off first so it will freeze solid. This is also a good way to use the left-over wine that is not good enough to drink anymore, but is fine for cooking.

Red wines should be chilled about 30-45 minutes in the refrigerator before serving, to about 62-65°F. You have probably heard that red wines should be served at room temperature, and you are right. However, the term "room temperature" refers to rooms in Europe way back when, and they were around 60°F, not the 72-75° we find in modern-day America. The slightly colder temperature slows the evaporation of alcohol, thus improving the aroma and flavor, and making the wine smoother. Don't over chill; this makes the tannins in the wine taste rough and bitter.

Some reds are actually served chilled, sweet red wines like Pomegranate and Cranberry flavored reds and
Beaujolais, especially for summer drinking.