We present the results of an isophotal shape analysis of three samples of galaxies in the Coma cluster. Quantitative morphology, together with structural and photometric parameters, is given for each galaxy. Special emphasis has been placed on the detailed classification of early-type galaxies. The three samples are: i) a sample of 97 early-type galaxies brighter than m_B_=17.00 falling within one degree from the center of the Coma cluster; these galaxies were observed with CCD cameras, mostly in good to excellent resolution conditions; ii) a magnitude complete sample of 107 galaxies of all morphological types down to m_B_=17.00 falling in a circular region of 50arcmin diameter, slightly offcentered to the North-West of the cluster center; the images for this and the next sample come from digitized photographic plates; iii) a complete comparison sample of 26 galaxies of all morphological types down to m_R_=16.05 (or m_B_=~17.5), also in a region of 50arcmin diameter, but centered 2.6degrees West of the cluster center. The reliability of our morphological classifications and structural parameters of galaxies, down to the adopted magnitude limits, is assessed by comparing the results on those galaxies for which we had images taken with different instrumentation and/or seeing conditions, and by comparing our results with similar data from other observers.