The general rule is that reds should be served at room temperature while whites, rosés and sparkling should be served chilled following a spell (not days) in the fridge.
Softer and lighter bodied reds can taste very refreshing if slightly chilled. This is true in summer, when they warm up quickly in a glass.
Try chilling Beaujolais and other inexpensive, un-oaked and juicy style wines. Dry Sherries such as Fino, Manzanilla and dry Sercial Maderia are also delicious chilled.
Most sweet wines should be served chilled, as should pale dry Sherry.