Recently, various Kondo phenomena have been observed in semiconductor quantum dots. The conventional Kondo effect takes place when an electron spin 1/2 is localized in quantum dots due to the Coulomb blockade and coupled to the Fermi sea in the leads. A significant enhancement of the conductance to 2e2/h is observed by the Kondo effect. We study unconventional Kondo effects in multiband quantum dots, silicon quantum dots and carbon nanotubes. First, the electronic states in silicon quantum dots are examined. We find that the discrete energy levels are degenerate by the multivally structure (more than one bottom of conduction band) in silicon and that the exchange interaction is very weak between different valleys. As a result, different spin states are almost degenerate in energy when two electrons are accommodated in the degenerate levels. Then we discuss the enhancement of Kondo effect in two cases. For an odd number of electrons, a large Kondo effect is expected which stems from the interplay between spin and orbital degrees of freedom [SU(4) Kondo effect]. For an even number of electrons, another large Kondo effect is proposed with six-fold degeneracy where three spin-singlet states and a triplet state take part in. Finally, we discuss the experimental results of Kondo effect in carbon nanotubes.