Mitochondria produce ATP by respiration and the Kreb's cycle.
If you want some extra credit, the cytoplasm of a cell (the fluid cellular matrix) also produces ATP, but by glycolysis.
Sugar and oxygen are used in cellular respiration, and create 38 ATP molecules per molecule of glucose. 2 ATPs are generated by glycolysis in the cytoplasm... the by products feed into the Kreb's cycle, which occurs exclusively in the mitochondria, and produces 36 ATP.
