We present an analysis of the X-ray spectra of a sample of 37 observations of 26 Seyfert galaxies observed by XMM-Newton in order to characterize their iron K' emission. All objects show evidence for iron line emission in the 6-7 keV band. A narrow 'core' at 6.4 keV is seen almost universally in the spectra, and we model this using a neutral Compton reflection component, assumed to be associated with distant, optically thick material such as the molecular torus. Once this, and absorption by a zone of ionized gas in the line of sight is accounted for, less than half of the sample observations show an acceptable fit. Approximately two-thirds of the sample shows evidence for further, broadened emission in the iron K band. When modelled with a Gaussian, the inferred energy is close to that expected for neutral iron, with a slight redshift, and an average velocity width of ~0.1c. The mean parameters are consistent with previous ASCA results and support the idea that the broad components can be associated with the accretion disc. Before proceeding to that conclusion, we test an alternative model comprising a blend of three to four narrow, unshifted emission lines (including the 6.4-keV core), together with one to two zones of highly ionized gas in the line of sight. Around one-third of the objects are not adequately fitted by this model, and in general better fits are obtained with a relativistic disc line model, which has fewer free parameters. None the less we find that absorption by ionized gas affects the spectrum above 2.5 keV in approximately half the sample. There is evidence for multiple ionized zones in at least three objects, but in all those cases a blurred reflector is required in addition to the complex absorption. We also identify a number of narrow emission and absorption features around the Fe complex, and the significance and interpretation of these lines is discussed. After accounting for these additional complexities,we determine the typical parameters for the broad reflection. The emission is found to come, on average, from a characteristic radius ~15 rg and the average disc inclination is ~ 40°. The broad reflection is on average significantly weaker, by a factor of ~2, than that expected from a flat disc illuminated by a point source. Notwithstanding these average properties, the objects exhibit a significant and wide range of reflection parameters. We find that 30 per cent of the sample observations can be explained solely with narrow-line components, with no evidence for broadened emission at all. A further 25 per cent show evidence for significant broad emission, but at a characteristic radius relatively far from the black hole. The remaining ~45 per cent are best fitted with a relativistically blurred reflection model. In 12/37 observations the characteristic emission radius is constrained to be <50 rg , where the gravitational redshift is measurable. For at least this subsample, our observations verify the potential for X-ray spectroscopy to diagnose the strong-gravity regime of supermassive black holes.