We investigate ion and impurity transport in turbulent, possibly anisotropic, magnetic fields. The turbulent magnetic field is modeled as a correlated stochastic field, with Gaussian distribution function and prescribed spatial auto-correlation function, superimposed onto a strong background field. The (running) diffusion coefficients of ions are determined in the three-dimensional environment, using two alternative methods, the semi-analytical decorrelation trajectory (DCT) method, and test-particle simulations. In a first step, the results of the test-particle simulations are compared with and used to validate the results obtained from the DCT method. For this purpose, a drift approximation was made in slab geometry, and relatively good qualitative agreement between the DCT method and the test-particle simulations was found. In a second step, the ion species He, Be, Ne and W, all assumed to be fully ionized, are considered under ITER-like conditions, and the scaling of their diffusivities is determined with respect to varying levels of turbulence (varying Kubo number), varying degrees of anisotropy of the turbulent structures and atomic number. In a third step, the test-particle simulations are repeated without drift approximation, directly using the Lorentz force, first in slab geometry, in order to assess the finite Larmor radius effects, and second in toroidal geometry, to account for the geometric effects. It is found that both effects are important, most prominently the effects due to toroidal geometry and the diffusivities are overestimated in slab geometry by an order of magnitude.