There is only one characteristic that is common to all lipids, and that is their inability to dissolve in water. They will, however, dissolve in a variety of organic solvents, such as benzene, acetone, alcohol, carbon tetrachloride,and chloroform. This single commonality is generally used to classify something as a lipid.
Beyond that one charcteristic, lipids display a wide variety of structures and features. They include oils, fats, and waxes; they can be liquid or solid at room temperature, and they may have other functional groups of various kinds attached. One example of this would be the phospholipids that comprise the majority of the cell membrane. In these membranes, it is the fact that lipids are chemically incompatible with water that actually helps to create the structure of the membrane.