We theoretically examine electronic states and Kondo effect in silicon quantum dots, taking into account a multivalley structure of conduction band. In the quantum dots, discrete energy levels are almost degenerate owing to two equivalent valleys. When an electron occupies the levels, an enhanced Kondo effect of SU(4) symmetry is expected. When two electrons are accommodated in a quantum dot, three spin-singlet and one spin-triplet states can be six-fold degenerate since the exchange integral is negligible when the dot size is much larger than the lattice constant of silicon. An underscreening Kondo effect involving these states is realized if tunnel couplings are equivalent for the levels. Otherwise, a "two-stage Kondo effect" is observed as a function of temperature, reflecting two independent SU(2) Kondo effects.