If a phone charger (or any electric adapter that is not connected to a device, for that matter) is plugged into an outlet, does unplugging it constitute any forbidden form of work, or is simply a 'muktzeh' issue? If it is a muktzeh issue, can it be unplugged and moved if the space is currently needed?
If the charger has an indicator light it would obviously be forbidden as unplugging would extinguish it. Even if not, phone chargers utilize electricity even when the phone is not plugged in. Consequently unplugging would interrupt the flow of electricity and would most probably be forbidden on Shabbos under the general minhag/uvdin dechol prohibition of utilizing electricity.
[Those that follow the Chazon Ish would regard this as an Issur Deorasa of Soser. Menuchas Ahava 24:2, quoted here writes that since people regard electricity as fire, it is forbidden to terminate an electric current as this is perceived as extinguishing fire. This answer rules that unplugging electrical devices is forbidden on Shabbos.]