Optogalvanic laser spectroscopy has been applied to measure the hyperfine structure of 13 spectral lines of Sc I in the wavelength range from 645 to 780 nm. Experimental magnetic dipole hyperfine structure constants A of the isotope Sc-45 have been determined for three levels of even and ten levels of odd parity. For six of these levels the A constants have been measured for the first time. For two further levels the A constants have already been measured but discrepancies between our values and the previous ones are found and discussed. With the new experimental results a parametric analysis of the magnetic dipole hyperfine structure has been performed for the even configuration 3d(2)4s and a very high value for the contact parameter a(3d)(10) has been found. Additionally, the experimental results for the other even levels are discussed.