My stock answer to this question is that you should choose the language that you are most motivated to speak, in terms of enjoying the cultures where it is spoken. It is useless to try to learn a language if you are not interested in the people who speak it. However, here is my list as I see it:
1. French. It is easy to learn because so many of it's words have entered English that the vocabulary is very familiar. It is used as a second language in various countries around the world, and the knowledge of French will increase your knowledge about Western culture in general.
2. Spanish. By far the most useful language if you are traveling in the Americas, but of little use elsewhere. It is a beautiful language and easier to learn than most.
3. Italian. My personal favorite, because of the deep cultural significance, but of limited value. Only spoken in Italy and thereabouts. It is beautiful, it is the easiest language to learn, and as it is the closest to latin, it is the key language that will open up all the other latin languages for you, if you choose to learn another one in the future.
4. Portuguese. One of the largest languages in the world is often overlooked. It is spoken in many countries in Africa, and Brazil and elsewhere.
5. German. For it's cultural worth, and because it is often a second language in Eastern Europe.
6. Japanese. If you are interested in learning about Japan it is essential. It would also be good for employment opportunities.
7. Russian. A very interesting and significant language, but rather difficult to learn. It is important to learn if you are traveling in the former Soviet Union, but not widely used outside of there.
8. Korea. Well, something had to be last. I am not sure what use Korean would be outside of Korea. But at least the written characters should be a lot easier to learn that Chinese or Japanese.