Dennou Coil is a 2007 anime by Madhouse, cryptically subtitled COIL A CIRCLE OF CHILDREN, which indeed follows a circle of children (and some adults) involved with mysteries related to cyberspace-viewing glasses and the strange beings reflected in them. Along the way it manages to explore themes of compassion, coming of age, and the nature of reality. The show's also known as Cyber Coil, which makes sense because attaching den- (electric- or cyber-) to the front of anything and everything is kind of a running theme.
As a quick aside, I had been kind of thinking about watching this show for a while, but receiving it as a recommendation Reverse Thieves' Anime Blog Secret Santa project was the impetus that forced me to get around to it. I also intend to watch and maybe review the two other recommendations I received, the Ghibli-sans-Miyazaki1 movie Only Yesterday and Yoshitoshi ABe's classic Haibane Renmei — but not before Christmas. As it is, with this season of anime being particularly above average in the number of enjoyable shows, and DJ Max Technika 2 also releasing around Thanksgiving and subsequently commanding a shameful amount of my time, I ended up putting off the show until the last few days and watching 23 of the 26 episodes in a whirlwind of 2 days.