This paper describes the determination of the ionization threshold of rubidium Rydberg atoms in crossed electric and magnetic fields. An experimental setup is used that allows one to count separately Rydberg atoms which ionize in the region of optical excitation, and those which leave the excitation region in a bound state. The obtained spectra allow one to determine the energy and the width of the ionization threshold. For different values of the electric-field strength E the influence of the magnetic field B on the ionization threshold was investigated. It was found that the scaled electric field \ensuremath{\epsilon}=${\mathit{EB}}^{\mathrm{\ensuremath{-}}4/3}$ and the scaled energy \ensuremath{\omega}=${\mathit{WB}}^{\mathrm{\ensuremath{-}}2/3}$ with excitation energy W are sufficient in order to describe the observed ionization threshold. This is remarkable since \ensuremath{\epsilon} and \ensuremath{\omega} are the classical parameters of the system. For \ensuremath{\epsilon}\ensuremath{\gtrsim}1.5 (atomic units), i.e., a weak magnetic field, the ionization energy does not depend on B and can be explained classically by direct-path ionization. In the regime 1.5\ensuremath{\ge}\ensuremath{\epsilon}\ensuremath{\ge}0.2, the energy and the width of the ionization threshold increase with increasing magnetic-field strength.In that regime the observed ionization behavior is qualitatively consistent with the assumption that the excited states are coupled to the continuum via free-electron states which exist at and beyond the classical ionization saddle point, those states corresponding to classical drift trajectories. At \ensuremath{\epsilon}\ensuremath{\approxeq}0.2, the ionization energy takes a maximum value, and in the range 0.2\ensuremath{\ge}\ensuremath{\epsilon}\ensuremath{\ge}0.06, with increasing magnetic field, both the energy and the width of the ionization threshold decrease again. A further increase of the magnetic-field strength changes the tendency a second time: for \ensuremath{\epsilon}0.06, both the ionization energy and the width increase again. In this high-magnetic-field regime the ionization energy was explained by classical drift trajectories which almost completely surround the Coulomb center and extend into the continuum. Wave functions of corresponding drift states were calculated using a Born-Oppenheimer approximation. The coupling between the inner-configuration-space volume and the drift states, which leads to ionization, vanishes in the classical limit.