What are the types of cellular respiration?

The two types of cellular respiration are aerobic and anaerobic respiration. 

1. Aerobic respiration occurs in the presence of oxygen to convert fats and sugars into chemical energy. Glucose reacts with oxygen, forming ATP to be used by the cell. This type of respiration takes place in the majority of plants and animals. Water and carbon dioxide are formed as end products of the process. Aerobic respiration is highly efficient (generating 36-38 ATP), and forms much more ATP than anaerobic respiration does. The reason for this is that oxygen is an ideal electron acceptor for the reactions that take place to form ATP.  
2. Anaerobic respiration breaks down sugars to produce energy without the use of oxygen; this process occurs in prokaryotes such as bacteria and archaea. Additionally, this type of respiration uses electron acceptors which are not molecular oxygen. For example, archaea such as methanogens utilize carbon dioxide as their final electron acceptor, forming methane as an end product. Sulfate is another commonly used final electron acceptor used by microorganisms, as they reduce it to hydrogen sulfide. Anaerobic respiration is much less efficient than aerobic respiration, as it only forms 2 ATP molecules.