I actually just became a DS9 fan in 2011. I had heard of it, of course, but for some reason had never thought of watching it when it originally aired.
It was late May/early June of 2011. I had just watched a bunch of my TNG episodes for the 1,000th time and I was thinking about what to watch next. Because of the TNG/DS9 crossover episode that featured Bashir, I started to read a little bit about DS9 to see if it was worth watching, and boy am I glad I did. I heard about things like the Dominion War, obviously, from it being mentioned in the movies, and I also read that Patrick Stewart was in the first episode of DS9, and that Worf joins the cast later on. So with these things in mind, I went on Youtube to watch "Emmisary" and after I watched it, I thought to myself, "this is pretty cool." So I bought the first season and started to watch it. Before I knew it, I had bought the entire series, and I spent the summer of 2011 watching it, a few episodes a day after work. The series has now become my absolute favorite out of all of Trek. As many people have stated already, I think it had the best character development out of any of the series, and I like that it took Trek in new directions that it had not been before. I love that it is basically one long story line with a bunch of smaller story lines mixed in. I love the diverse cast, the re-occurring characters, the beautiful sets, everything!