We examine emission-line profiles observed with the Solar Ultraviolet Measurement of Emitted Radiation (SUMER) instrument during the roll of the SOHO spacecraft on 1997 March 20. SUMER data were acquired in selected wavelength bands including lines from the low chromosphere to the corona. Our main aim is to determine the center-to-limb behavior of emission lines formed in the chromosphere, transition region, and corona, especially of the observed Doppler shifts, to try to form a consistent picture of the basic kinematic properties of the emitting plasmas. To achieve this we combine the roll data with data from the full disk discussed elsewhere and fitted Gaussian profiles to the cores of the line profiles. The Doppler-shift data at large spatial scales (>50'') clearly reveal center-to-limb redshift behavior consistent with a cos variation in all transition region lines. The three "coronal" lines in the data set (of Ne VIII and Mg X) reveal center-to-limb behavior consistent with disk-center blueshifts, in contradiction to some previous work. The redshift to blueshift transition occurs at electron temperatures of about 5 × 105 K. Furthermore, we present evidence for an outflow of the fast solar wind from the coronal holes throughout the whole transition region. These results confirm and extend earlier work and point toward a (re-) measurement of rest wavelengths of lines formed at coronal temperatures in the laboratory. Together these results provide a firmer observational foundation for the development of classes of models to account for the well-known redshifts and point to the need to develop models that can also account for the coronal-line blueshifts.