Correlation coefficients enable to you find relationships between a wide variety of data. However, the sheer number of options can be overwhelming. This picture sums up the differences between five of the most popular correlation coefficients. Part two covers several less popular correlation coefficients.

Further reading:

Gamma & Coefficient & Yule's Q

Kendall's Tau

Pearson Correlation

Spearman's Rank Correlation

References:

A comparison of the Pearson and Spearman correlation methods

Nonparametrics Statistics Notes - Correlations (Spearman, Kendall t...

Kendall’s Tau and Spearman’s Rank Correlation Coefficient