Can I use PCA (or should I use regression) for testing the effect of multiple variables on one dependent variable? I have 2000 soil property measures and 14 different variables like rainfall, temperature, slope, etc. I want to check the effect of those 14 variables on soil property measures, including which variable affects my soil property the most. Is PCA a suitable solution to this? Or should I try multiple regression instead?
 A: Though multiple regression is generally better, allowing you to extract more meaningful and interpretable information from your model, it does have its weaknesses. It may not do a very good job if you are expecting interactions or nonlinear shapes, because you may not have sufficient power even with 2000 points (I would do a power analysis to be confident about this). It's also difficult if you don't have clear hypotheses about those interactions or the shapes of the responses. 
However, you probably should be most concerned about multicollinearity, i.e. non-trivial correlations among your 14 explanatory variables. This last case is where a PCA is likely to be helpful. It allows you to break apart correlated variables into orthogonal vectors that can then be used without problems in regressions. These regressions may be single or multiple - you can, after all, use more than one PCA axis as a predictor variable. 
So to sum up: it's not an either/or. Check for multicollinearity, and if it is present, you can do a PCA followed by a multiple regression.
EDIT based on Ian_Fin's suggestion below. 
It is possible to interpret the variables in a multiple regression that uses PCA axes as explanatory variables, because the PCA tells you the strength and direction of each underlying variable's contribution to each axis (the loadings). In practice, though, this can be tricky and will depend on the underlying correlation structure. 
A: If I'm understanding your problem, you have 14 explanatory variables and just one response variable. That kind of problems can be addressed by multiple regression. Principal component analysis is useful to classify observations, reduce the number of variables and understand how a set of variables are related to each other, but not to explore the relation of one response variable to all the other.
