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.

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 tau, Gamma)

Kendall’s Tau and Spearman’s Rank Correlation Coefficient