  The electronic properties of the carbon substituted MgB$_2$ single crystals
are reported. The carbon substitution drops T$_c$ below 2 K. In-plane
resistivity shows a remarkable increase in residual resistivity by
C-substitution, while the change of in-plane/out-of-plane Hall coefficients is
rather small. Raman scattering spectra indicate that the E$_{2g}$-phonon
frequency radically hardens with increasing the carbon-content, suggesting the
weakening of electron-phonon coupling. Another striking C-effect is the
increases of the second critical fields in both in-plane and out-of-plane
directions, accompanied by a reduction in the anisotropy ratio. The possible
changes in the electronic state and the origin of T$_c$-suppression by
C-substitution are discussed.
