I'm familiar with the program and I know someone who taught on it.
The advantages:
You get to see a lot of different places
The people who teach on it are dedicated and internationally-minded
The disadvantages:
You don't get immersed in a foreign culture; it's more dash-on-to-the-next-place tourism
You're in school with Americans, just like at home
The academics are fairly so-so and the students tend to be more interested in partying than in cultural opportunities
I have quite a bit of experience in this whole field, and what I'd recommend above Semester at Sea is going on a study-abroad program that immerses you in one place you can get to know intimately, with lots of contact with the people who live there. Best would be one of the programs where you actually enroll as a student of a foreign university, which you can often do via your home university's study-abroad office. The Scandinavian countries are especially good for this, and university courses there are taught in English (though admittedly Scandinavian countries are expensive). Britain, Ireland, Australia or New Zealand are other good alternatives if you don't want to be operating in a foreign language. The fact that they're English-speaking may fool you into thinking the culture won't be that different, but this is an illusion — they are very, very different, and the whole experience will be disorienting in just the reason people benefit from going abroad.
Second choice would be a program in which you mix with people from other nations, even if the program is meant for foreigners, for instance the program for French learners at the Catholic University of the West in Angers, France (a very good program).
Last choice would be a program just for Americans in a foreign country, where at least you get to spend intensive time getting to know a place intimately and having a chance to meet some local people.
The Semester at Sea is not a badly run program, but it doesn't really offer these other advantages.