My understanding is that geometry relaxation (i.e. letting the nuclei follow the force gradients of the PES until they reach local minima) should usually be performed in order to get the correct molecular or material energies from electronic structure calculations.
Are there times when doing so would actually give an incorrect/inaccurate answer?
One example that I can think of (which may be incorrect) would be when trying to study molecular ionization by an applied electric field. That is, the electronic dynamics may be so fast that the nuclei would not have the time to respond to the forces before the electron actually leaves the molecule. Thus, to get an accurate understanding of the electron dynamics, you should not let the nuclei relax. To get the final, post-ionization molecular energy, though, you would want to let the nuclei relax again.
Are there other, less clear, situations?