To me, and again this is someone who has watched every series, every movie, and over 95% of the episodes in most of the series (TOS, TNG, DS9, VOY, and ENT), I couldn't wait until DS9 was on the air. I was so glad to be there to watch the crew go through their ups and downs and it did tell stories that spoke to the human condition--even in some respects more than the rest of the series ever dared touched upon. On DS9 we got to see it all, war, religion, pain, love, loss, and hope. Me personally, I am a 9er and I will forever be. It took nearly three seasons for it to find it's place, but like TNG, that's when everything got better. With the addition of the Defiant (my #2 favorite ship), Worf in season 4 and the Dominion War, I think it not only made the series more solid, I think it made it more deep. Not only that, you had storylines in DS9 that you never saw on the earlier series (i.e. Dominion War, the Maquis, The Circle) just to name a few. We got to learn not only the good side of the Federation but it's darker side as well with the introduction of Section 31. I loved the fact that the Federation wasn't a perfect utopia that TNG made it out to be and one of the biggest episodes to make this point was the 2 part episode in season 4, 'Homefront' and 'Paradise Lost'.
But DS9 would be nothing without the characters and the large base of recurring characters that people came back week after week to watch for. The thing is, I in a way, owe DS9 a debt of gratitude. If it weren't for that show, I wouldn't be so interested in BC, doing fan fiction, or still love Star Trek as much as I do after over twenty years of watching it on TV. So, that is in a nutshell is why I think DS9 is the best Trek of them all.
Not to say that there's not a bad point in the show or two... But it is my favorite in my humble opinion.