LiveJournal
LiveJournal is one of the original mainstream blogging sites. It encourages original, long-form written content rather than one-liners and reshares, although it also enables media embedding so that users can easily link videos and music.
LiveJournal allows extensive use of HTML formatting, offers numerous customization options and uses tagging and "memories" to allow users to organize their posts. One of its most popular features is a set of powerful privacy filters that allow users to control who sees their content. Over the years, LiveJournal has upheld these filters and kept them easy to use. LiveJournal is free to use, but it also offers a premium version with no ads and additional features.
Blogger and WordPress
Blogger and WordPress are two of the best-known, general-purpose blogging websites. Like LiveJournal, they focus on long-form written content. Both have user interfaces with an intuitive, simplistic design, and the default layouts for both services are no-nonsense and straight to the point. Blogger is a Google-owned site, and if you already have a Google Account, you don't have to create a new one to use Blogger. Blogger's biggest disadvantage is that, unlike its competitors, it only allows the entire blog to be private or not, with no settings for individual posts. WordPress, in addition to allowing privacy settings for individual posts, is known for being extremely customizable and has an active user support community.
Tumblr
Tumblr is a blogging service as well as a social network. While it allows original, long-form, written content -- and some people use it this way -- it focuses much more heavily on resharing pictures and videos. It's easy to register on Tumblr and get started with basic posting, but overall the Tumblr user interface is less intuitive than those of Livejournal, Blogger and WordPress. The service's strongest features are its ease of resharing other people's content and a built-in "mailbag" option where blog owners can allow other users to submit questions or content. Users can make individual posts private if they want. Tumblr is free to use, and for teenagers, it's one of the most popular social media sites on the Internet. Be aware that Tumblr has a lot of adult content on issues like art, politics and sexuality, which may not be suitable for some younger kids.
Kid-Targeted Blogging Sites
If you have specific goals in mind, such as education or especially restrictive parental oversight, you can choose from a number of kid-specific blogging services. Doodlekit focuses on maximum parental control over the blogging environment, allowing you to restrict almost any aspect from privacy settings to forum moderation. This could be ideal for young children or for kids who need a lot of oversight. Alternatively, Kidblog and Edublogs both offer an academically oriented experience. Here, teachers retain administrative control, and students can develop their writing skills on private blogs visible only to their classmates and the teacher.
Safety and Oversight
If you're considering a kid-friendly blogging service solely on the basis of safety, it's probably okay to let your kids use a general blogging site instead. When it comes to hacker attacks, the big services usually have better security, and when it comes to predators or identity thieves, any website viewable to the public is a potential target, although having a public-facing site is an integral part of the appeal of blogging. You'll do better by teaching your children safe Internet behavior practices and monitoring what they write. Separately, note that United States law requires children under the age of 13 to obtain verifiable parental consent before publishing any personal information online. If you have kids younger than this, create the blog yourself and let them use your account to write posts -- perhaps in conjunction with you rather than on their own.