To start off, the story is pretty good. The anime slowly draws you deeper and deeper into the central mysteries of the series, always letting you know enough to keep you satisfied but not to the point where you can tie all the loose ends yourself. You always get the feeling that there is something deeper in the background, pulling the strings, manipulating the protagonists like a bunch of puppets.
The main storyline has several branches: a search for what killed Kenichi's childhood friend, and the resolution of Isako's brother's fate. This puts the anime on a rather tragic path, but surprisingly the writers manage to keep the emotional appeal stable, never letting the anime descend for too long into excessive melodrama at the expense of the sense of fun and adventure of childhood that the series is fundamentally about.
There are many side stories interspersed throughout the series. Most of them are interesting and woven quite well into the overall framework (eg The Last Pleiosaur being one of my favorites), but a few of them are kind of sleep-inducing (mostly due to poor pacing), to be honest. This is especially the case towards the early middle of the series, which was when I stopped watching for a couple months, only coming back later to finish. Some of the stories have a "slice of life" kind of feel, and I'm not a particular fan of that genre, so maybe that explains it.
The art is fantastic. It is very reminiscent of Miyazaki's style for some reason, and in fact the storytelling itself feels very much the same. Dennou Coil is like My Neighbor Totoro meets Mushishi, with a strange cyber twist. Don't get the wrong idea though. The series is not cyberpunk. The anime is not gritty, though it can be dramatic. There is no attempt to really explore the implications of AI or emergent behavior. The nature of objective reality, and its relationship to virtual reality, is examined, but the themes and the conclusions drawn are more akin to classical Japanese fantasy than cyberpunk.
For instance, one unique part of Dennou Coil's fictive universe is the meta-tags, which are apparently snippets of code on ofuda scrolls or something similar (ofuda scrolls are those things that Rei from Sailor Moon uses, in case it isn't clear). Another example would be the spirit-like "null illegals" that wander the obsolete cyberspace. These are clearly inspiration from Shintoism and, while they are interesting, they are part of a large reservoir of reasons why the universe feels like a wannabe fantasy world rather than a real cyber world. All the tech is just magic with a modern twist. Don't expect anything to make real scientific sense. Instead, see Dennou Coil for what it really is: a beautiful supernatural story recasted in modern terms. It succeeds wonderfully in this regard.
Some who have seen the anime will notice that some interesting parallels can be drawn to Fullmetal Alchemist. The "encode" system utilized by some of the hackers in Dennou Coil is very similar to the alchemy system in FMA. Interestingly, the symbols and patterns, despite being apparently pretty much just magic, are justified as "science" and technology in both series. Like Fullmetal Alchemist, Dennou Coil is also very much a "coming of age" story that has somewhat dark tones occasionally, especially towards the end. So I would suggest that fans of FMA take a look at Dennou Coil, though it's definitely not going to be the cup of tea of every FMA fan.
The music and the sound effects are generally good but not outstanding. The opening and ending, however, are absolutely wonderful. They project an aura of mystery and hopeful melancholy that captures the spirit of the series very well.
The characters in Dennou Coil are quite good. Sometimes during the series I felt like, somewhere, sometime, somehow, these people could actually really exist. The circle of children is composed mainly of girls and they all act realistically for the most part. Don't expect the stereotypical bubbly lolis you see in a lot of modern anime. The characters are charmingly human in their range of emotions and will feel quite familiar.
My only complaint with regards to characterization is Isako. She was a much more interesting, respectable character before the series made her out to be a tsundere. Personally, I felt this transition deviated too much from her original presentation, and rather than adding depth to her personality, turned her into a stock character. But aside from this, I would say that the characterization in the series is very strong.
Overall, this is one of my favorite anime series so far, but I don't think it's for everyone. If you are a fan of "coming of age" stories and/or enjoy Miyazaki movies (in particular the aforementioned My Neighbor Totoro), this is a must watch. If you like FMA, you might like this. If you enjoy science fiction, you might like it, as long as you don't place too high a premium on plausibility. Last but not least, if you found the strange universe of Mushishi fascinating, you might also like the universe in Dennou Coil. As for myself, I fit in all those categories.
