What relationship is there between two variables -one of which is X and the other X^2- in OLS regression

[Gabriel Klein]

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For example what impact would including AGE and AGE^2 have on a model...

[Nick Cox]

It depends. Note that age and its square can easily be almost collinear, depending on the incidence of ages.

[Carlo Lazzaro]

Gabriel:
too broad a question with no data example.
Usually, you include both linear and squared terms (via -fvvarlist-, pregerably) for -age- to investigate whether the relationship between this predictor and the regressand is non-linear.
Issues like centering -age- around a meaningful value (or moment distribution, such as mean) and/or collinearity, as Nick helpfully anticipated, cannot be ruled out on a priori basis.