Density Functional Theory (DFT) has become the favorite tool for computational studies on larger molecules. This is mainly due to its low order scaling of the computational cost and to the fact that an interpretation of the results in terms of molecular orbitals is possible in contrast to other methods, which go beyond the mean field approximation for the electron-electron repulsion. However, no systematic hierarchy of methods exist within the framework of DFT. Therefore it is not possible to check the accuracy of a particular DFT method by going to a higher level method in the same hierarchy, but one has to compare to either experimental results or results of correlated wavefunction methods. In my presentation I will discuss such comparisons with results from high level Coupled Cluster calculations including triple excitations for electronic excitation energies, NMR chemical shifts and indirect nuclear spin-spin coupling constants as well as ESR hyperfine coupling constants. I will try to address the question of the accuracy, which one can expect of DFT calculations of these spectral properties.