It would depend on whether symmetry is important to what you're trying to do (e.g., identifying the correct electronic state). Make sure you're not imposing a symmetry artificially, though, as this can lead to incorrect solutions sometimes. For example, if you run an optimization in C2v symmetry then it will find a stationary point on the C2v potential energy surface. However, if the molecule does not have that symmetry, this will be a transition state position on the Cs or C1 potential energy surface. If the system really does have symmetry and you're using a method that is reasonably well defined within various approximations, running without symmetry will usually (approximately) recover the correct symmetry of your system, but you can't take this for granted and will have to check your solutions to make sure they are physically reasonable.

For slab-gap calculations (necessary in 3D pbc such as with plane-wave codes) sometimes it may help to create a slab with inversion symmetry to avoid any issues with surface polarization. If you are looking at (potentially) polar surface terminations then of course you don't want this symmetry :) and you may consider switching to an LCAO-based periodic DFT code such as CRYSTAL, FHI-AIMS, or ADF-BAND.