Consider using the linear measures below if your variables satisfy linear assumptions (e.g. variables have normally distributed residuals and the relationships between your variables are linear). Also, attempt to minimise the number of double zeros shared between variables. For example, consider removing variables or objects with many "0" values. Bear in mind, that any such modification of your data will impact the measures.
Pearson's r

This familiar measure of linear correlation between two
variables, suitable only for detecting linear relationships between
variables. This is covariance between two variables divided by the
product of their standard deviations. If your variables have many zeros,
this correlation coefficient will not be reliable as doublezeros will
be understood as an "agreement" when, in fact, they are simply the
absence of an observation. This will inflate the correlation
coefficient.

Covariance

The
unstandardised form of linear correlation, or the covariance, between
variables may also be used. Variables should be centred on their means
(i.e. all variables have a mean of "0") before calculating covariances
as an Rmode measure. 
Consider using the rankorder correlation coefficients below if linearisation fails or if you have many variables with many "0" values.
Spearman's rho 
This is a nonparametric measure of correlation which uses ranks rather
than the original variable values. Variables should have monotonic
relationships: that is, their ranks should either go up or down across
objects, but not necessarily in a linear fashion. Like Pearson's r,
Spearman's rho is based on the principal of least squares, but is
concerned with how strongly the rankings between two variables disagree.
The larger the disagreement the lower the rho value. This statistic is
sensitive to large disagreements. That is, if one variable ranks an
object as "1" and another variable ranks the same object as "100", the
correlation reported by Spearman's rho will be strongly affected
(relative to Kendall's tau, for example), even if these variables agree
on all other ranks. This measure is suitable for raw or standardized
abundance data and any monotonically related variables.


Kendall's τ 
Like the Spearman's rho, Kendall's tau uses ranked values
to calculate correlation. This measure, however, is not based on the
principal of least squares and instead expresses the degree of
concordance between two rankings. The tau statistic is the quotient of
1) the difference between concordant and discordant pairs (i.e. ranks
that agree and ranks that differ) and 2) the total number of pairs
compared. This statistic is not sensitive to the scale of the
disagreement. As above, variables
should have monotonic relationships: that is, their ranks should either
go up or down across objects, but not necessarily in a linear fashion. This measure is suitable for raw or standardized abundance data and any monotonically related variables. 
