Cunard does "scheduled trans-Atlantic crossings" with the Queen Elizabeth 2 (to be replaced for this purpose by the Queen Mary 2 from 2004).

Also, all of the major American cruise lines which operate northern summer cruises in the Mediterranean have trans-Atlantic positioning cruises at the beginning and end of the season. Each ship will cross from the Caribbean (typically) to Europe for the summer, and will then return to the Caribbean afterwards (often via a short stint doing New England in the autumn). Look for eastbound crossings in March/April/May/June and westbound crossings in September/October/November each year. Just from memory, you will find these on Celebrity, Holland America, Princess, Norwegian Cruise Line and Royal Carribean - and probably others too. All you need to do is search their websites.