Nonparametric procedures are applicable to data with far fewer assumptions than the usual classical procedures.
They are less sensitive to departures from the assumptions.
In testing, the level is maintained even if the assumed model is incorrect.
Estimators and test statistics are less sensitive to extreme or unusual observations.
Simplicity and intuitive nature of the procedures.
Applicable to specific types of data for which classical procedures are not. e.g., rank and count data.
Technology advances have increased accessibility for the general practitioner. (Bootstrapping, resampling, and simulation are becoming more common.)
Many nonparametric tests, intervals, statistics, confidence bands, and multiple comparisons procedures are distribution-free. Roughly speaking, this means that these methods do NOT depend on the specific distributional form of the population.