When can (or should) I use a functional language?

I'd like to to propose an open discussion on this topic. I've heard this question raised often, both by those who are contemplating learning a functional language, and by those who already have the skills but are still apprehensive about the appropriate way to apply them.

• Are functional languages suitable for general purpose programming, or only specific use cases?

• What projects would benefit the most from a functional language?

• Can I introduce a functional language into an existing project?