Laboratory experiments on decaying quasi-2D (two-dimensional) turbulence have been performed in stratified fluids in both square and circular containers. The turbulence was generated by towing an array of vertical cylinders through the container, which was filled with either a two-layer or a linearly stratified fluid. By varying the grid configuration a different amount of angular momentum could be added to the initial flow. The evolution of the flow was visualized by 2D particle tracking velocimetry. The observed decay scenario has been investigated with emphasis on the evolution of the kinetic energy and the enstrophy of the horizontal flow, vortex statistics and the angular momentum of the flow. In particular it is shown that the experiments in both the square and the circular container support the observations from numerical simulations of decaying 2D turbulence in bounded domains with no-slip walls. Two striking examples are the experimental observation of the spontaneous spin-up phenomenon (in the square-container experiments) and the confirmation that the angular momentum of the flow in the circular-container experiment is better conserved than the total kinetic energy of the flow. The role of the initial nonzero net angular momentum on the decay of quasi-2D turbulence is investigated for both geometries and indications for an acceleration of the self-organization process are presented.