Most of the good sites for children, sadly but not surprisingly, are American. Or Canadian: YES Mag, "Canada's Science Magazine for Kids", is one of the best, with lots of stimulating stuff - explanations of how things work, paper plane designs, seriously worthy features on structures, brain teasers.
Kid'n Around, spun off from America's "premier newspaper for kids and their families", also has some science content, but is a stylishly plain general magazine with a monthly theme (eg adventure), explored through departmentalised features that contain lots of relevant links. For once, a site where content seems more important than presentation.
In sharp contrast are two sites (not strictly zines, I guess) that aim to stimulate children by offering them the opportunity to create the content of the site - an excellent idea, from the perspective of the visitor to the site as well as the contributors. The two sites seem to occupy much the same territory, while having rather different atmospheres.
Kids' Space deliberately encourages international involvement, with flag graphics to identify where the stories, pictures and music come from. With nursery colour schemes and a Guide Bear to explain what's what, the site seems to be pitched at relatively young children, but the contributions come from quite a range of ages. Cyberkids has a slightly more grown-up feel, at least on the opening pages, and has one or two elements handed down from grown-ups - but both deserve exploration by kids in the six to 10 range, I'd say.
KidsNet is home-grown. It is aimed not so much at children as parents with the threat of boredom looming, calling itself "The Weekly Family Guide to 'Days Out' and 'What's On' all over the UK". It has a searchable directory of such things as museums and sports centres, but the content is laughably thin outside London - no zoos in the South-west, for example. (If things to do in London are what you're after, look at Kids Out Online, too.)
Incidentally, a word of warning for those concerned about what else children might find on the Web: be aware that search engines can throw up all sorts of unpredictable results. In the course of preparing this article, for example, I searched for "child magazine"; among the sites thrown up was Erotic Desires - "The Hottest Gay Sex Magazine On The Internet". There are software systems for blocking access to X-rated sites, but that's another story.
YES Mag http://www.islandnet.com/yesmag/
Kid'n Around http://www.kidnaround.com
Kids' Space http://www.kids-space.org
Kids Out Online http://www.kidsout-london.com