Meteorology.
Often we’re checking how well different instruments measuring the same condition (temperature) agree with each other. In some cases we may have a negative correlation if we are measuring different states, such as: when temperature goes up relative humidity goes down.
The R coefficient of correlation is more useful with one predictor variable and one determined variable, it can have useful negative values. R-squared is superior when there may be more than one predictor variable contributing to the determined variable. One predictor may go up and another down but both contribute to the determined value.
The R and R-squared values are both useful tools for slightly different questions.