1. if you want the statistical significance of an expected difference between two normally distributed random variables.
2. if you want a measure of linear association of two (actually also normally distributed) random variables (Pearson's r) or if you want a measure of monotone association of two (arbitrarily distributed) random variables (Rank correlation measures like Sprearman's rho).
3. if you want the statistical significance of the reduction in the residual variance that is attributable to one ore more predictors in a linear model.
4. if you want to express how different the odds of an event are in diffrerent groups or under different conditions.