The temperature dependence of the London penetration depth,lambda(T), was measured in both single crystal and polycrystalline MgB_2 samples by a high-resolution, radio frequency technique. A clear exponential temperature dependence of lambda(T) was observed at low temperature, indicating s-wave pairing. A BCS fit to the lowest temperature data gives an in-plane energy gap Delta of 2.6\pm0.2 meV (2\Delta/T_c=1.5\pm0.1), which is significantly smaller than the standard BCS weak coupling value of 3.5. We find that the data are best described by a two-gap model.