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Raspberries (and blackberries and all those similar) have a short shelf life which is why you rarely see them sold in stores. They might last a day or two but go bad fast (even with refrigeration.) Blueberries also go bad quickly but can last a bit longer. Yes, refrigerate them, but don't wait too long to eat.
A simple rule of thumb is that fruits from temperate climates tend to refrigerate well, while fruits from warm climates do not. So, refrigerate tree fruits such as apples, plums, pears and cherries. All commercially important berries in North America also benefit from refrigeration.