You can just use the "regular" correlation coefficient (Pearson), but if your variable is a categorical one that represents an increasing/decreasing "quantity" or "frequency," then Spearman's rank-correlation coefficient will provide more meaningful results.
Even when you do an ANOVA, which is usually just for categorical independent variables with continuous dependent variables, the software usually provides a calculation of r and r^2.
There are many different correlation coefficients, depending on the variable types and the levels of measurement:
point biserial -> dichotomous indep variable, continuous dependent variable
phi -> both variables are dichotomies
biserial -> same as point-biserial, but assumes an underlying "continuity" for the dichotomous variable
tetrachoric -> same as phi, but with the assumption of an underlying "continuity"