Aims. We study the transition region (TR) properties above sunspots and the surrounding plage regions, by analyzing several sunspot reference spectra obtained by the SUMER (Solar Ultraviolet Measurements of Emitted Radiation) instrument in March 1999 and November 2006. Methods. We compare the SUMER spectra observed in the umbra, penumbra, plage, and sunspot plume regions. The hydrogen Lyman line profiles averaged in each of the four regions are presented. For the sunspot observed in 2006, the electron densities, differential emission measure (DEM), and filling factors of the TR plasma in the four regions are also investigated.Results. The self-reversals of the hydrogen Lyman line profiles are almost absent in sunspots at different locations (at heliocentric angles of up to 49 • ) on the solar disk. In the sunspot plume, the Lyman lines are also not reversed, whilst the lower Lyman line profiles observed in the plage region are obviously reversed, a phenomenon found also in the normal quiet Sun. The TR densities of the umbra and plume are similar and one order of magnitude lower than those of the plage and penumbra. The DEM curve of the sunspot plume exhibits a peak centered at log(T/K) ∼ 5.45, which exceeds the DEM of other regions by one to two orders of magnitude at these temperatures. We also find that more than 100 lines, which are very weak or not observed anywhere else on the Sun, are well observed by SUMER in the sunspot, especially in the sunspot plume. Conclusions. We suggest that the TR above sunspots is higher and probably more extended, and that the opacity of the hydrogen lines is much lower above sunspots, compared to the TR above plage regions. Our result indicates that the enhanced TR emission of the sunspot plume is probably caused by a large filling factor. The strongly enhanced emission at TR temperatures and the reduced continuum ensure that many normally weak TR lines are clearly distinctive in the spectra of sunspot plumes.