The magnetic hysteresis and the temperature-dependent magnetization of interacting nanoparticle assemblies are studied by Monte Carlo simulations. By comparison of the simulation results with measurements in Fe/Ag samples grown by low energy cluster beam deposition demonstrate that interparticle exchange interactions dominate over the dipolar interactions and are responsible for the collective magnetic behavior in this system. The simulation of the magnetic properties of quasi-two-dimensional ordered arrays of Co nanoparticles, prepared by self-assembly from a colloidal dispersion, demonstrates that dipolar interactions are responsible for an increase of the blocking temperature relative to the isolated particles. The collective behavior is manifest by oscillations in the magnetization with increasing layer coverage.