To answer your question, I imagine there are several million Earth-like planets in the Milky Way, and that's a very conservative estimate.
Combine that with the fact that 100 billion other galaxies each harbor several million Earth-like planets, and you're left with that familiar feeling of overwhelming smallness that cosmology so typically imparts us with. This is in our observable universe alone; there are likely other galaxies and who-knows-whats outside of our visible horizon in the universe, not to mention the infinite multiverse hypothesis.
I like to say that when it comes to space-time and civilizations, there's too much space and not enough time... that is, the distances separating intelligent life are so daunting that it requires a species to reach a technologically mature level prior to their ability to make contact with other species. It's probably safe to assume that with technological maturity comes ethical maturity, which is why I find the beloved scenario of aliens attacking Earth for its resources pretty outlandish.
Great production, thanks for spreading the gospel of science!