Last minute cruises are one of the best ways to find a bargain. Cruises don't always sell out, and when they don't, the cruise line sometimes cuts prices to fill the remaining cabins.
A disadvantage of trying for a last minute deal is that the selection is not great. You're picking through the "leftovers" so to speak. You also have to be ready to go on relatively short notice. Many of these bargains appear only 30 days before the ship sails.
Some cruise lines have officially ended the practice of offering last minute deals. On their ships, people who book early get just as good deals as those who wait.