Old thread, but...
Only some of the hard science is out of date, because Cosmos also contains a number of tales from the past, while speculating on how things might be, had those tales turned out differently. It manages to do this without being preachy in a way that only Sagan could do, and as far as I can know, no one really has done since.
Cosmos places importance in using your imagination to figure out new things, and how imagination was used to first discover the Earth's place in the solar system. Sagan spends considerable time imagining our planet from an alien's point of view and flies around the galaxy in a "ship of the imagination", all this without being cheesy or silly.
Cosmos encourages you to ask questions, just like Eratosthenes did about the length of the shadow of a stick put in the ground at noon at different locations in the world, which then led to discovering that the surface of the Earth was curved. It's hugely inspiring, because it's not told as a curiosity of the past, but as an example of how the principles of science are ageless.
There is so much of it that is extremely relevant today, where it seems that fewer people place significance on science and more on religion.
Agree with poster above. For me, it's not necessarily the conclusions presented but more the path Sagan takes to get there that excites me about Cosmos. I'm 33 years old and never saw Cosmos growing up, but I have an affinity towards Sagan after reading a couple of his books. That feeling grows when watching him present and narrate on Cosmos, he's a phenomenal speaker/ teacher.