In this paper, we propose a paradigm of control, called a maximum hands-off control. A hands-off control is defined as a control that has a short support per unit time. The maximum hands-off control is the minimum support (or sparsest) per unit time among all controls that achieve control objectives. For finite horizon continuous-time control, we show the equivalence between the maximum hands-off control and L-1-optimal control under a uniqueness assumption called normality. This result rationalizes the use of L-1 optimality in computing a maximum hands-off control. The same result is obtained for discrete-time hands-off control. We also propose an L-1/L-2-optimal control to obtain a smooth hands-off control. Furthermore, we give a self-triggered feedback control algorithm for linear time-invariant systems, which achieves a given sparsity rate and practical stability in the case of plant disturbances. An example is included to illustrate the effectiveness of the proposed control.