Can you travel a cruise ship around Europe for a whole year?

Considering that ships only sail to and from certain ports, the entirety of Europe's costal areas can be covered in much less than a year. You could do it, if you booked several concurrent cruises on a variety of ships.

*A* cruise ship, as in one ship? Probably not. Most ships sail the same route over and over again, so you wouldn't be sailing "around" Europe. In fact, the majority of the ships are only in Europe for the summer. You'd have to book a series of cruises on different ships, and might even have to spend some time at a hotel on land if the arrival date of one ship isn't the same as the departure date of the next.

yes and no. there are a few world cruises out there but they are not sold as one itinerary, but many legs. and they may start in europe but they don't stay there in winter. you can book back to back cruises on the same line for as many weeks as you can afford and ships tend to repeat the same 2-3 itineraries all season long( summer in Europe, winter in the caribbean)

You can also buy a condo of sorts on a cruise ship named "The World" . You buy it for a year. BUT it would cost you more then one million dollars. It doesn't stay in Europe but travels the world. Not many cruise ships go to Europe during the winter months anyways. I believe Cunard is the only one and they just keep going back and forth across the Atlantic. There are always people who stay on a certain ship for 6 months or longer. They are usually retired with lots of money. They simply book back to back to back, etc on the same ship.