I find the Love It or Hate It debate over this anime hilarious, but I also REALLY get it. On the one hand, this anime is beautiful. The art and sound production is fantastic, especially from a smaller studio. The action is (overall) very well done. They have a really good pace, and they feel frenetic and exciting. It doesn't just excel at action either, there are many genuinely touching moments in this series.
Of course, I can also see the hate. While they do a lot of little design things with the MMO concept, they don't do much in the overall story. The first season is full of time skips that make you go, "Wait what! All of that intervening time!" The second season has excessive fanservice, and a change to the game makes it much less dramatic or intense. The show is very mixed, character-wise. On one end there's Suguha, who is easily the most developed character in the show, while still managing to be sympathetic, likable, and engaging. (Even if her subplot does give me the oogies.) Near the middle is Asuna, who starts off interesting, disappears for a while, reappears and is kinda meh, before growing into something better. But then, there are the problem characters. First off is the protagonist, Kirito. He feels REALLY inconsistent. Early on there's his loner thing, there's the people dying complex he develops, and there's his romance. Besides that...his personality seems to completely change depending on the episode, or sometimes scene, he's in. And the season two villain! My friend who got me into this show used to rave to me about how evil he was, and how much I'd hate him. He's half right. Dude's definitely evil, but after a while I gave up hating him. He's a cartoon. He's a silly caricature of what "evil" is. His motivations are weak, and he has absolutely no redeeming qualities. In other settings with different styles, that could work, but this show's tone clashes with that. You can only add so many Villain tropes to one character before they stop being empathetic, and once you can't even empathize with a character, your ability to like or dislike them is sorely diminished.
Overall, I liked Sword Ass (I mean Art) Online. I'm glad I saw it. It's pretty flawed, but the emotion and drive it presents combined with the fantastic action makes me enjoy it regardless. To me it feels like Gurren Lagann wearing a really shiny .hack/sign suit. That leads to the problem, however, that Gurren Lagann works as well as it does because it doesn't give a rat's ass about how it looks, or the believability of it's story. SAO lacks that quality to make up for it. What it really needs is to be dubbed and put on Toonami. Put it in with that crowd, and it's going to stick out, and in a good way. If you know you're someone who can't get over logical or character problems in a show, this isn't for you. But if you can dip yourself into this world and enjoy the emotional roller-coaster, it comes recommended.