I have recently finished re-watching Babylon 5 on Hulu. They only have the first two seasons, which means that the episodes they have leave off right about where I think the series began to become really interesting. But one thing I have noticed even in just watching those two seasons is how well the series holds up. Some of the effects would be done differently today, but the series still works, and for the reason it struck science fiction fans as so good originally.
First, the alien life is richly imagined. This is actually fairly rare in science fiction for TV, which tends to be humans with alien dressing. In Babylon 5 the alien races and alien politics are often more interesting than the politics of Earth, which is just one strand in the tapestry. You get a rich sense of the Centauri, of the Narns, of the Minbari, and even of the mysterious Vorlons, much richer than you get of aliens in other series, even in just the first two seasons.
Second, the plot is truly character-driven. Already in the first two seasons you get Londo, likable but driven by ambition, already pushed by his ambitions into going past the point of no return on the path of monstrous atrocity, already beginning to realize that he has let himself be caught up in a process that will inevitably turn him into a lonely monster who has done deeds even he loathes. He is one of the few villains science fiction for which one can feel a truly whole-hearted sympathy and pity. And, while G'Kar will have a long ways to go we already see him beginning to be tried in the fires of tribulation that will, once he finds his way past his thirst for vengeance, make him the sage he will eventually become. And there are plenty of other characters who are fascinating in their own right.
And third, while the profundity of science fiction is often exaggerated, its potential for profundity is not, and while Babylon 5's own depth, like the depth of any other franchise, is limited by the depth of thought of those who made and wrote it, by both a happy choice of ideas and a sort of dogged insistence in dealing with them, B5 really does do well in the deep ideas department, continually exploring those two most dangerous questions: Who are you? What do you want?