Studies of the ground and excited states in semiconductor quantum dots containing 1 to 12 electrons showed that the quantum numbers of the states in the excitation spectra can be identified and compared with exact calculations. A magnetic field induces transitions between the ground and excited states. These transitions were analyzed in terms of crossings between single-particle states, singlet-triplet transitions, spin polarization, and Hund’s rule. These impurity-free quantum dots allow "atomic physics" experiments to be performed in magnetic field regimes not accessible for atoms.