  (abridged) We present deep spectroscopy of a large sample of low-metallicity
emission-line galaxies. The main goal of this study is to derive element
abundances in these low-metallicity galaxies. We analyze 121 VLT spectra of HII
regions in 46 low-metallicity emission-line galaxies. 83 of these spectra are
archival VLT/FORS1+UVES spectra of HII regions in 31 low-metallicity
emission-line galaxies that are studied for the first time with standard direct
methods to determine the electron temperatures, the electron number densities,
and the chemical abundances. The oxygen abundance of the sample lies in the
range 12 + log O/H = 7.2-8.4. The Ne/O ratio increases with increasing oxygen
abundance. The Fe/O ratio decreases from roughly solar at the lowest
metallicities to about one tenth of solar, indicating that the degree of
depletion of iron into dust grains depends on metallicity. The N/O ratio in
extremely low-metallicity galaxies with 12+logO/H<7.5 shows a slight increase
with decreasing oxygen abundance. We present the first empirical relation
between the electron temperature derived from [SIII]6312/9069 or [NII]5755/6583
and the one derived from [OIII]4363/(4959+5007) in low-metallicity galaxies. In
a number of objects, the abundances of C^++ and O^++ could be derived from
recombination lines. Our study confirms the discrepancy between abundances
found from recombination lines (RLs) and collisionally excited lines (CELs) and
that C/O increases with O/H.
