Polar cruises include trips to both Antarctica and the Arctic. You just don't think about a cruise to the polar regions in the same way you think about the Caribbean. Given how special they are it is pretty surprising how many companies go there and how quickly their cruises sell out.
You won't find many mass market ships in these area of the world. Most ships that sail these waters are specially constructed to withstand an occasional collision with an iceberg (kidding, kidding) but they do often have reinforced hulls and special equipment for dealing with the cold.
Cruiselines offering Polar cruises include:
Abercrombie & Kent - charters the La Boreal for its Arctic and Antarctic cruises. It is the first all balcony ship to sail in these waters. As with the other trips offered by A&K, luxury is the key. They do have a first class collection of group leaders and lecturers to help bring the area to life.
Hurtigruten - is known for their Norwegian coastal cruises but they have one ship, the MS Fram, that offers expeditions to Antarctica, Greenland, and Spitzbergen.
Lindblad Expeditions - has been sailing to Antarctica for many years - it is practically where the company got it's start. They also have itineraries to the Arctic.
Orion Expeditions - has a single ship that sails from Australia while the "jumping off point" for the other lines is South America.
Alaska Dream - operates 3 small ships in Southeast Alaska. Their tag line is "True Alaska with true Alaskans". They offer 8 to 13 day cruises focused on spotlighting scenic beauty, amazing wildlife, and intriguing native culture.
Cruise North - Cruise North Expeditions operates a single ship, Sea Adventurer, which accommodates 118 passengers. The ship is specially designed for arctic expedition cruising. Her ice-strengthened hull permits her to glide easily and safely through ice-strewn waters that are not accessible to conventional cruise vessels.
Quark Expeditions - Quark Expeditions is known as the premier company specializing in polar expeditions. They operate 5 ships in Arctic and Antarctic and offer different levels of adventure, from the traditional soft adventure experience to camping in a tent on Antarctic ice. There are several reasons that the company is considered the leader in Polar expeditions. One is their fleet - all specifically designed to operate in polar waters. Another is the variety of their options for different experiences - from luxury cruises to environments that are more like an experience on a research vessel.
Seabourn Cruise Line - offers several Antarctica itineraries that include several ports in South America. Their approach emphasizes scenic cruising as opposed to lots of zodiacs and hiking on glaciers.
Travel Dynamics - sends one of their luxury small ships to Antarctica each year. They do plan for landings every day while they are in Antarctica and have a staff of study leaders and naturalist guides on board to help bring experiences to life.