  The discovery of over 200 extrasolar planets with the radial velocity (RV)
technique has revealed that many giant planets have large eccentricities, in
striking contrast with most of the planets in the solar system and prior
theories of planet formation. The realization that many giant planets have
large eccentricities raises a fundamental question: ``Do terrestrial-size
planets of other stars typically have significantly eccentric orbits or nearly
circular orbits like the Earth?'' Here, we demonstrate that photometric
observations of transiting planets could be used to characterize the orbital
eccentricities for individual transiting planets, as well the eccentricity
distribution for various populations of transiting planets (e.g., those with a
certain range of orbital periods or physical sizes). Such characterizations can
provide valuable constraints on theories for the excitation of eccentricities
and tidal dissipation. We outline the future prospects of the technique given
the exciting prospects for future transit searches, such as those to be carried
out by the CoRoT and Kepler missions.
