In this thesis we study many-body effects in three distinct two-dimensional systems. The two dimensional electron gas is a model system yielding to basic analytical and computational theoretical ideas of many-body physics and at the same time allows faithful experimental realizations. In connection to the recently observed metal-insulator transition in this system, the spin susceptibility is a relevant observable. The behavior of the spin polarization in a parallel magnetic field is studied using a parametrized ground-state energy expression from accurate quantum Monte Carlo simulations and compared with approximate theories. The critical field to fully polarize the system is calculated. A qualitative difference for the ferromagnetic transition is found for an interval of density values. Next, we consider exciton condensation in an electron-hole bilayer system with density imbalance. Electrons and holes attracting via Coulomb interaction pair up to form spatially separated excitons and condense at low temperatures. Using mean- field theory we establish the phase diagram at zero temperature for different electron and hole densities by comparing the energy of the normal phase with that of the condensed phase. In the last chapter, the two-dimensional Bose-Fermi atomic gas mixture which is composed of a condensed boson component and a spin polarized Fermi component at zero temperature is studied. Confinement in the third direction affects the density profiles and can induce collapse of the mixture and spatial separation of components.