Why is my r² value so low, even though the line comes close to my points?

Some users have noted that their linear regression analysis returns an unexpectedly low value for r² even though the regression line appears to fit the data points well.

This can happen when the slope of the line is very low, and indistinguishable from zero. The quantity r² measures the degree to which knowing X helps you predict Y. If the slope is near zero, then knowing X does not help you to predict Y. So even though the line fits the data well, the r² is (appropriately) low.