Hiking equipment
According to Tom Brown, the basic plan for survival is in the order of shelter (including clothing), water, fire, and food. Cody Lundin writes about the "Rule of 3s"; this relates to human survival without basics: three minutes without air, three hours without shelter, three days without water, or three weeks without food.
Hydrothermal vent
While chemosynthesis occurring at the deep ocean allows organisms to live without sunlight in the immediate sense, they technically still rely on the sun for survival, since oxygen in the ocean is a byproduct of photosynthesis. However, if the sun were to suddenly disappear and photosynthesis ceased to occur on our planet, life at the deep-sea hydrothermal vents could continue for millennia (until the oxygen was depleted).