When there is a good operational reason, and you are properly prepared, running a tank dry is a good idea. At the first moment the engine begins to stumble fuel from another tank should be appied in accordance with the flight manual procedures.
When ferrying aircraft I used to do this regularly on alternaing tanks, to determine how long the engine would run, once "empty" was indicated. This was helpful to the other ferry pilot who took the plane long over water distances on the next legs.
When I flew the C310, I would do this regularly to confirm that tanks were empty, to optimize range.
As long as the engine is not trying to develop high power for long on no fuel, it will be fine. These things are considered during certification. Keep it to a minimum though.
In terms of a caution, do not begin this process, and forget you are doing it. It can be really disconcerting to have it quit turning base, or entering a hold, because you forgot what you were doing. If your phase of flight changes, or the workload goes up, select the fuller tank, and leave the experimentation to another flight. Also, warn your passenger that is what you are doing, before the engine stumbles, so as to not alarm them.