Nitpicking aside, this is a serious anime, with spectacular animation and contains enough dramatic tension to keep viewers hooked. If I were going to pick any show on American TV similar to this, I'd have to go with AMC's The Walking Dead. There are a lot of major deaths in the show, and the tone is very bleak. Often times anime shows will teeter between cheerful and dramatic, and more often than not this is a failure. This show doesn't pull any comedic punches, and since my humor is very different than that of the Japanese, I was glad there wasn't any.
Similar to The Walking Dead, there are some real dull moments, especially about 3/4s of the way in. Characters could use a bit more development, and the world's mythology could be a bit more fleshed out. Since I haven't read the manga (japanese comics), I can't argue that this isn't explained, but being that I have seen all there is to offer as a complete show, it feels very incomplete. Once again, I'm referring to the show, not the ongoing manga. I hope that this isn't the end of the series, but I won't hold my breath.
Overall, if you are into anime, this is a must. If you are hesitant about anime, I'd say give it about 3-4 episodes (each one is about 25 minutes long). I also am stopping the rating system on this site, because I think that it cheapens the art form to rank quality.