I have been learning how to program some in C++ to eventually program games, but then I got to thinking of a future goal I had of making a 3D world where up to say 16 people can be connected. The idea is to create a small multi-player RPG. I planned to try using OpenGL once I have a decent grasp of C++ programming to make some small games and work my way to my goal, but I wasn't sure if, when using OpenGL and C++, I would be accomplish my future goal. What I am asking is this: Would it be possible to make this game without having to involve other languages or scripts?

From a not-too-skilled coder:

Remember that the stereotypical advice here is:
Q: "I want to make an MMORPG!"
A: "Don't!"

...Partly because it's really hard. You're talking about combining RPG mechanics, 3D graphics, and networking, each of which is tough in its own right. So, it's fine if you think of it as a long-term goal (especially if you're looking at more like 16 players than 16,000), but still, understand that you're picking possibly the most complex type of game out there.

Yeah, I think that OpenGL and C++ together will let you do that if you've got the skill. For relative simplicity though you might want to use Ogre3D (which can use OpenGL and automates some tedious tasks), or another engine atop OpenGL. I don't know your current skill level, but if you haven't done so already I suggest trying to make games, period, before you try to make 3D games. Have you got the basic mechanics of a playable game down yet? It'll be really hard to try to learn those things at the same time as OpenGL and C++ and networking.