When correlation turns too high? It is possible to find a lot online on intepreting correlation coefficients. But I find often difficult to decide when to drop a variable from a linear model because of its correlation with another variable.


*

*What should I consider in defining a threashold for the correlation
coefficient?  

*What coefficient (0.4?) should I generally use to define two variables as "too" correlated?

*What practical suggestions should I follow in a correlation analysis
of my variables?

 A: Some correlation is not a problem. Actually, it is the very reason why we add control variables. Consider what would happen when all explanatory variables are not correlated with one another. In that case there would be no added value to adding them all in one model: you could just look at a series of bivariate regressions and get the same results. So, the idea of adding control variables to your model only makes sense if the variables are correlated with one another. 
An extremely high correlation may cause problems with the way computers handle numbers. However, algorithms for computing linear regression have improved that much that that is in most cases not a problem. A correlation of .4 is no where near that mark (think .99 or .999).
Moderate correlation means that there is less information which your model could use to disentangle the effects of two correlated explanatory variables than you would have expected based on the sample size alone. As a concequence the standard error will be high and confidence intervals will be wide. That is an unfortunate but accurate representation of the amount of information you have available. So if you are not collecting the data yourself there is nothing you can do and there is nothing you should do about that.
However, if your variables are moderately correlated you might want to consider the possibility that they are actually measuring the same thing. In that case you would either want to use that to get a better estimate of that one thing (a measurement model in a SEM for example) or choose just one of these variables. Imagine how you would interpret your results when you add both: the effect of a unit change in one measurement of a concept while keeping the other measurement of that same concept constant...
