The npc companions you meet and can take with you along the way and their interactions with each other were great and enhanced further by an NPC banter mod that is popular among those who mod the game.
'Party interactions' came down to a single sentence exchanged between NPCs from time to time. There was nearly no character development of any sort. Talking to NPCs consisted of them throwing a wall of text at you and your answers were: I accept, I'm a dick or I refuse. Oh then there was goodbye. Seldom did the game give you any actual choice, let alone a dialogue. I have played the first Fallout just before playing BG, and after all the praise I have heard for BG, it felt incredibly simplistic and underwhelming: By its story, world and characters. It was bland and it was generic. The only reason why I have finished playing BG is the fantastic NPC mod and very solid exploration factor, which, in my case, could not carry the entire game by itself.
And here we are getting to how 'innovative' BG was: I'll take this straight out of SimonG's mouth, because I agree 100%. BG was to RPGs of its day what Halo of Modern Warfare is to FPS of today: It made BG accessible to a wider audience, it streamlined the genre. There was nothing innovative nor revolutionary about it. Before BG, there were games like TES: Daggerfall, Fallout, Ultima series, Betrayal at Krondor, just to name those that I have personally played (and aside from Fallout, all of them AFTER BG.) There were loads, and loads did precisely what BG, but in a more complicated and not as pretty manner. But they did do it better, or at least as far as I am concerned. If you'd like a straight parallel to BG, it would probably be Betrayal at Krondor, which had exploration, party-based tactical combat, NPC interactions and an utterly fantastic story - aside from user friendliness, it beats BG at every turn.
Bear with me, because now I'm FINALLY getting to why do I think that BG doesn't really have anything to offer today: First of all, there's BG 2, which just does what the first game, but flatout better, aside from exploration factor (I still didn't enjoy it because of the generic setting, but it improves unpon the original tremendously.) And now modern games, be it Dragon Age or Neverwinter Nights 2, just offer a better, more polished experience than the first BG. As all it was about was polish... It just doesn't really have much of a place anymore. Still, the game is most definitely not bad, and there are going to be people who are just more prone to liking it.