We have computed evolutionary models for extrasolar planets that range in mass from 0.1M_J to 3.0M_J and that range in equilibrium temperature from 113 to 2000 K. We present four sequences of models, designed to show the structural effects of a solid (20 M_⊕) core and of internal heating due to the conversion of kinetic to thermal energy at pressures of tens of bars. The model radii at ages of 4-5 Gyr are intended for future comparisons with radii derived from observations of transiting extrasolar planets. To provide such comparisons, we expect that of order 10 transiting planets with orbital periods less than 200 days can be detected around bright (V < 10-11) main-sequence stars, for which accurate well-sampled radial velocity (RV) measurements can also be readily accumulated. Through these observations, structural properties of the planets will be derivable, particularly for low-mass, high-temperature planets. Implications regarding the transiting companion to OGLE-TR-56 recently announced by Konacki et al. are discussed. With regard to the transiting planet HD 209458b, we find, in accordance with other recent calculations, that models without internal heating predict a radius that is ~0.3R_J smaller than the observed radius. Two resolutions have been proposed for this discrepancy. Guillot & Showman hypothesize that deposition of kinetic wind energy at pressures of tens of bars is responsible for heating the planet and maintaining its large size. Our models confirm that dissipation of the type proposed by Guillot & Showman can indeed produce a large radius for HD 209458b. Bodenheimer, Lin, & Mardling suggest that HD 209458b owes its large size to dissipation of energy arising from ongoing tidal circularization of the planetary orbit. This mechanism requires the presence of an additional planetary companion to continuously force the eccentricity. We show that residual scatter in the current RV data set for HD 209458b is consistent with the presence of an as-of-yet undetected second companion and that further RV monitoring of HD 209458 is indicated. Tidal circularization theory also can provide constraints on planetary radii. Extrasolar giant planets with periods of order 7 days should be actively circularizing. We find that the observed eccentricities of e ~ 0.14 for both HD 217107b (P = 6.276 days; M sin i = 1.80M_J) and HD 68988b (P = 7.125 days, M sin i = 1.29M_J) likely indicate either relatively small planetary radii for these objects (R ~ 1.1R_J) or tidal quality factors in the neighborhood of Q_P ~ 10⁷. For these two planets, it will be difficult to differentiate the contribution from tidal and kinetic heating. But the radius of HD 168746b (P = 6.403 days, M sin i = 0.23M_J) is sensitive to whether the planet's interior is heated by tidal dissipation or kinetic heating. The tidal circularization timescale of this planet is shorter than the age of its host star, but we show that within the observational uncertainties, the published RV data can also be fitted with a circular orbit for this planet. As more RV planets with periods of order 1 week are discovered, Q_P(T_eq,M_P) and R_P(T_eq,M_P) will become better determined.