The consensus among biochemists is that virtually every cell in the human body can break down sugar, usually in the form of glucose, to use as energy. According to the authors of the 5th edition of "Biochemistry," the brain and the kidneys prefer to run on glucose. In fact, the brain favors glucose to such an extent that it only metabolizes other fuel sources after several days of starvation.
Unlike the brain, "Biochemistry" indicates that many other organs prefer alternative metabolic fuels before turning to glucose. One of the best understood examples of this phenomenon is the liver. As the major organ of metabolism, the liver processes most of the nutrients obtained from food in the digestive tract. Rather than use glucose to fuel its own activities, the liver stores incoming glucose as starch, called glycogen. Once glycogen stores are full, additional glucose is converted directly to fat. The liver prefers to use ketone bodies and other byproducts of metabolism as fuel.
Skeletal muscles burn glucose as well as fatty acids and ketone bodies for fuel. Compared to skeletal muscle, cardiac muscle contains very little glycogen and instead prefers medium chain fatty acids as its fuel of choice. Similarly, the cells in adipose tissue, which hold most of the fat reserves in the body, seldom use glucose for fuel. Instead, adipocytes rely on the energy stored in triacylglycerol droplets to synthesize and store fatty acids as a long-term energy reserve.