Respiration is not essential for life. Many forms of bacteria do not undergo cellular respiration and are still considered 'alive'. Respiration, more specificially cellular respiration, is just one of many ways (although one of the more energetically efficient ways) for a cell to produce energy.
Human cells are capable of producing energy in one of two ways, depending on the condition the cells are placed in. The most common of the two ways is through cellular respiration. This occurs when there is sufficient oxygen being carried to the cells via the blood. The second occurs when the body's cells do not have enough oxygen to support cellular respiration. This is commonly experienced during heavy workouts. When the body's cells don't have the needed oxygen to undergo cellular respiration, the cells revert to a form of energy creation called 'fermentation,' which DOES NOT require oxygen. Fermentation causes the build-up of lactic acid in muscle cells, which leaves that sore feeling in your muscles after a workout.