Yes, and no.
If you are 19, and are married, many of the cruise lines will make an exception to the rules if you and your spouse go together.
Disney and Cunard have some select cruises that allow someone as young as 18 to sail by themselves. These cruise lines are pricey, and it's only on certain cruises that they allow this.
There are a very small handful of companies that offer Tours For Teens. One such company is Rein Tours. http://www.reinteentours.com These companies are very similar to sending a kid away to summer camp. They are expensive, but they are very good programs. Teens travel across the country in a group with chaperons, they stay in various hotels, they tour across the country. Some of their programs include a short cruise which is chaperoned by the adult counselors. I don't know if it's possible to do just the cruise, or if you would be obligated to do the entire tour(s) that their programs offer. That is something you would want to ask them.