Polarization-dependent x-ray-absorption spectroscopy on the O 1s and Cu 2p edges using the non-surface-sensitive fluorescence method has been performed on single crystals of ${\mathrm{La}}_{2\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Sr}}_{\mathit{x}}$${\mathrm{CuO}}_{4+\mathrm{\ensuremath{\delta}}}$, ${\mathit{R}}_{2\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Ce}}_{\mathit{x}}$${\mathrm{CuO}}_{4\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\delta}}}$ (R=Nd and Sm), and the insulating compound ${\mathrm{Ca}}_{0.86}$${\mathrm{Sr}}_{0.14}$${\mathrm{CuO}}_{2}$. The experimental results support the picture of a doped charge-transfer insulator. The symmetry of hole states on O and Cu sites has been determined. These have predominantly in-plane, i.e., O 2${\mathit{p}}_{\mathit{x},}$y and Cu 3${\mathit{d}}_{\mathit{x}}^{2}$-${\mathit{y}}^{2}$ character. In p-type doped cuprates for 0x0.15 about 8% of the total number of hole states on O sites have O 2${\mathit{p}}_{\mathit{z}}$ character, which probably originates from apical O sites. At higher dopant concentration, this number increases. In the n-type doped system 4--11 % of the O 2p states in the energy range of the upper Hubbard band have O 2${\mathit{p}}_{\mathit{z}}$ character. In nearly all the systems investigated in this work the fraction of unoccupied Cu 3${\mathit{d}}_{3\mathit{z}}^{2}$-${\mathit{r}}^{2}$ states with respect to the total number of Cu holes in the upper Hubbard band is 3\ifmmode\pm\else\textpm\fi{}3 %. At higher energies a high spectral weight with Cu 3${\mathit{d}}_{3\mathit{z}}^{2}$-${\mathit{r}}^{2}$ character (about 40% of the total amount of unoccupied Cu 3d states in the upper Hubbard band) is observed, which is probably caused by a hybridization with Cu 4s and 4p states. The implication of holes in nonplanar orbitals on high-${\mathit{T}}_{\mathit{c}}$ superconductivity in cuprates is discussed.