We present ultrahigh-resolution spectra for a set of nearby F-G-K stars on, or close to, the main sequence. The wavelength shifts of stellar lines relative to their laboratory wavelengths are measured for more than a thousand Fe I lines per star, finding a clear correlation with line depth. The observed patterns are interpreted as convective blueshifts that become more prominent for weaker lines, which are formed in deeper atmospheric layers. A morphological sequence with spectral type or effective temperature is apparent. Two K giant stars have also been studied. The velocity span between weak and strong lines for these stars is larger than for the dwarfs and subgiants of similar spectral types. Our results show that convective wavelength shifts may seriously compromise the accuracy of absolute spectroscopic radial velocities but that an empirical correction may be applied to measured velocities.