Most cruise lines don't permit passenger to bring power strips. While technically it's usually surge-protectors they don't like, often any power strip-looking device is confiscated by ship security, along with extension cords (which may be why other power strips are taken, too).
You can read more about the safety regulations that drive these policies here.
What are alternatives to power strips on cruise ships?
There are a number of options, but one of the simplest (and smallest - which is nice for packing) is to take advantage of the fact that most modern-electronics that don't generate heat (such as hair irons) can operate on 220v, the voltage commonly used in Europe. This means a simple adapter like the one below can give you two additional outlets in your stateroom without taking up a single regular outlet.
This adapter, along with other items to make your cabin that much more comfy and convenient, are below. You can also visit the CuirseHabit Shop for a full selection of cruise shirts, accessories, and more!