The possibility of using a measure of integration $\Phi$ independent of the metric is studied in gravity theories. These theories give rise naturally to a vacuum with zero energy density. Scale invariant (s.i.) actions are studied and it is found that s.i. can be spontaneously broken classically. These s.i. models give: (i) a cosmological see saw effect for obtaining a state with a very small vacuum energy density, (ii) quintessential cosmological scenarios without the long range force problem and (iii) a natural explanation of the origin of the three fermionic families of particle physics. String and brane theories can be formulated using these types of measures. In the resulting theories, the tension becomes a spontaneously generated quantity.