For most everyday cooking oils, the safest bet is a cool, dark and dry place, such as a kitchen cabinet or pantry. Keep the container tightly sealed and away from the stove, oven, dishwasher and direct sunlight. Buying smaller quantities can also make sense if you use oil slowly. A large bottle that takes many months to finish may spend considerably longer exposed to oxygen after opening. And while refrigeration can extend the life of some oils, it is not necessary for every type. Some oils may become cloudy or solidify when chilled, so storage recommendations can vary.
The oil beside your stove is not necessarily bad simply because it has been sitting there. But heat and light can shorten its useful life, particularly when exposure happens day after day. Moving the bottle into a cool, dark cabinet, keeping the lid tightly closed and buying quantities you can reasonably use before they deteriorate are small changes that can make a difference.