Based on what I've heard from top devs - Lua (supergood for devs), C# and C++ are three. Then learn SQL, XML, etc to support your projects. Also (if you're a gamedev) learn at least 1 game engine, like Unreal Engine or Unity. Even Gamemaker is worth it, at least for prototyping. But again, that's coming from others not me. I'm no expert.

It depends on what you're programming. Knowing a language is one thing, but knowing how to code is quite a different thing. There's abstractions and paradigms you need to understand, clean code, proper commenting, architecture, etc etc. Don't worry though, it'll all come in due time. Just keep at it.

Learning a new language after you learned your first one is proportionally easier. Especially after learning something comprehensive like C++ or even C#. I'm guessing a "functional language" (like (edit:) F#) is also nice to know, depending on your specific field. But don't take my word for it.

1 minute ago, ApochPiQ said:

D is not a functional language by any stretch of the imagination. It is much more procedural/OO in the vein of C++.

Sorry, I guess I meant F#. My bad and fixed.

C++ is a multi-paradigm language. From wiki:

Even if it does not support (yet) paradigms like aspect programming, or will never go into the imperative paradigm, or its syntax is not as cleaned as some "theoretical-oriented languages", to my opinion, this is a language one must know.

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What languages should a person learn to be a well-rounded programmer?

Languages don't really make you a better programmer, concepts, techniques and algorithms do. Different languages are a proxy for this, as they bundle up opinionated implementations of a selection of concepts, techniques and algorithms.

What you want to look for are different languages that espouse complimentary sets of concepts and techniques, and solve challenging problems using similar algorithms in them—so that you get a sense for how different languages (again, as proxies for concepts and techniques) occasion different implementation strategies.

Good question, though.

My general recommendation is that to stay relevant developers should learn one new programming language every year.  Even better if it is a departure from things already comfortable with, but the key factor is that you keep learning.

Right now as a general recommendation, new programmers should first learn ALL of these languages: C++, Java, C#, C, JavaScript, Python, and SQL, and also learn markup languages including HTML, XML, and JSON. In all these languages a programmer should be fluent enough that if handed some code they could read it and expand on it, even if it isn't their primary programming language.

In practice an entry level programmer will probably know two or three of them, but they should still learn those they don't know, and continue learning at about one per year.  I see it as much the same a doctor must stay current on medical research, or the way a lawyer must stay current on new laws and new precedent, or the way an architect must stay current on architectural codes.  

How many or which languages you know is not what makes a good programmer though- it's about how you employ those languages to accomplish whatever your task or goal is.