How do you determine if you should use a quadratic term or a cubed term?

[Steve Mikos]

Is there a test to determine if you should use a quadratic term or a cubed term?

[Joseph Coveney]

I suppose that you could "test" whether the regression coefficients for the polynomial terms are "statistically significant", but why not just, say, examine residuals-versus-fitted plots with and without the polynomial terms?