1200 calories per day is about the lowest a woman should go when aiming for fat loss. This level of calories has been found to help with weight loss in trials.
For men this figure is around the 1500-1700 calorie mark. This varies greatly depending on your height, weight, and level of physical activity. It is advisable to find your individual calorie needs rather than going by generalized guidelines.
Taylor, C. B., Agras, W. S., Losch, M., Plante, T. G., & Burnett, K. (1991). Improving the effectiveness of computer-assisted weight loss. Behavior Therapy, 22(2), 229-236. Link
Epstein, L. H., Valoski, A. M., Vara, L. S., McCurley, J., Wisniewski, L., Kalarchian, M. A., ... & Shrager, L. R. (1995). Effects of decreasing sedentary behavior and increasing activity on weight change in obese children. Health psychology, 14(2), 109. Link