I don't think there should be any surprise what my answer is. (NB: I originally composed this for my blog; no one who reads over there has watched the show.)
So, in trying to think of reasons for why this show is so great, I settled on a couple different things. One, and the one that most impressed me, is how amazingly well it maintains its own continuity. I'm used to things like, say, finding out Scully got her cross on her fifteenth birthday and then three seasons later it was on Christmas; or Bill Adama's first wife was Carol, and his second wife was Anne, but then he just had the one wife named Carolanne. On Babylon 5, a conversation between two characters in the pilot ends up paying off three episodes from the series finale; a minor comment turns into a life-saving moment twenty episodes later; a C-plot that seemed to only exist to help round out a new character becomes a major, major plot point nearly two seasons down the road.
It's this astonishing level of detail that allows the show to sustain arcs that span thirty or forty episodes; nothing is forgotten or left behind, there's no retconning to make things work, because the writer didn't make things up as he went along. J. Michael Straczynski, who wrote 92 out of 110 episodes (and every episode aside from one in seasons three, four and five), planned the entire series out like a novel. Foreshadowing, rising tension, see a gun in act one and watch it go off in act three; everything was set up in a very deliberate, calculated way, and once the series really gets going midway through S2, it doesn't stop.
Besides the plot, there's also wonderful characterization. People grow and change; their actions have consequences; relationships can get difficult, and they're not always pretty, but they're real. A lot of shows seem to have one voice, but everyone has their own distinctive voice on this show, which is a pretty remarkable feat, considering the number of different alien races. There are also some instances of just glorious writing.
(Another reason to love this show? Things rarely turn out how you'd expect. On most shows, the Battle of the Line would be a stirring military triumph as a last-ditch effort to save humanity prevails against overwhelming odds. The Line fails; out of 20,000 defenders, less than 200 survive. I won't spoil for you what does actually save the day; it's pretty much one of the major plot points of the whole series, and it's kinda awesome.)
Also, the female characters on this show rule. I mean, really, they rule.
And I know I posted this one as one of my top five quotes, but it's too awesome not to include. Also, there aren't a lot of action-y things I can post out of context, but I think this one plays. This is pretty much the greatest minute of the entire show, really; the episode as a whole won a Hugo, as well.
And the shippiness. Guys. Guys, listen. These two characters. Guys. Here's the best way I can sum up how great John/Delenn are: their first big real kiss? Comes after she gives him a fleet of warships, to be deployed under their joint command. Awesome.
(I even love the gag reels!)
This is not to say the show is perfect. It was a low-budget syndicated SF show in the mid-90s, and there are plenty of times you can tell, especially when it comes to the guest actors. There are a few episodes that just don't work, and one mini-arc that I wasn't fond of. But by and large? It is not hyperbole when I say that if I had watched this show when it actually aired, I think I would have loved it more than The X-Files.
Seriously, you guys. You guys, seriously.