As ridiculous as this might sound, it's a very viable option. Many people have heard of Beatrice Muller, a woman who retired and lived for years on the Queen Elizabeth II before it was decommissioned (in doing research, it appears that she is now too old to do this and is in an assisted care facility). However, it turns out that many others have "retired" to cruise ships. It's become popular enough that in 2004, a study was published entitled Cruise ship care: a proposed alternative to assisted living facilities. The study found that for many retirees, not only was living on a cruise ship as cost effective as a retirement home, it's also more effective at providing for quality of life for many people (though there comes a point where you can't physically do it any more).
For many retirees, they might be able to retired abroad to save money, but if you do that, you may not be able to have the constant travel you enjoy ... unless your retirement is constant travel.
If you don't mind a small bunk, with a tiny porthole, and making few, if any, long-lasting friends, and not being able to easily pop over and visit friends and family, perhaps a cruise ship is for you? Right now, prices for cruise ships are lower than ever (largely due to a lackluster economy and bad press for some cruises) and cruises offer frequent traveler discounts, so if sailing the high seas for the rest of your life sounds exciting and you have an adventurous spirit, this might be a bit more fun than sitting in a retirement home.