The rule of thumb that most of us follow when it comes to drinking wine is that white and rose wines and sparkling wines should be served chilled and red wines should be served at room temperature.
There are however some red wines that are better served chilled due to their natural high sugar composition such as the Italian Gragnano Penisola Sorrentina Doc.
Also, once you open a bottle of red wine and have some left, keep it in the fridge. The wine is still ageing but it oxidises at a slower rate than if it were left out.
When you're ready to drink the wine, take it out of the refrigerator about a half hour before serving to bring the temperature back up.
When it comes to chilling wine, specially for long periods of time, it is better to use a proper wine cooler as it is designed to maintain the right levels of humidity, usually at 57%. The standard kitchen fridge is fine to keep a wine for up to 3-4 weeks. Anything above that runs the risk of oxidising. This happens because normal kitchen fridges are designed to keep the humidity at 0% which dries out the cork allowing oxygen to get in.
Other tips about cooling wine
Always keep unopened wine with a natural cork lying down in the refrigerator so that the wine is always in contact with the cork.
Keep unopened wine in the most steady part of the fridge away from where the motor is or door shelves to avoid exposure to vibration.
When closing a bottle of opened wine, seal it as tightly as possible by putting the cork back in or using a wine stopper that fits really well.