In my first post on correlation coefficients, I outlined the differences between five popular coefficients: Pearson's, Spearman's Rank, Kendall's Tau, Gamma, and Yule's Q. There are many others to choose from, depending on what you're doing with your data. This one picture is a comprehensive overview of less popular correlation coefficients you may come across.

Further Reading:

Canonical Correlation

Coefficient of Determination (R^2)

Concordance Correlation Coefficient

Cramer's V

Intraclass Correlation

Moran's I

Phi Coefficient

Point Biserial

Polychoric Correlation

Tetrachoric Correlation