Lots of classical homeschoolers use the The Story of the Worldseries (link just goes to the first volume; there are four) for world history. We've been using it for nearly 4 years now.
There are lots of good things about this series. It's generally neutral- not Christian, but not anti-religious (I don't like either viewpoint when you're studying history- focusing on one religion's interpretation or ridiculing religion in general is a useless way to study history). It's appealing to children and a good introduction of world history. It has a lot of fun activities and is excellent for homeschooled or afterschooled children. In short, it really is the best world history curriculum for elementary children .
But this is not an unbiased view of history (it's not in depth either, but it shouldn't be when it's designed for children ages 6-10). Despite spending more time on places like Australia, India and Africa than your public school teachers probably did, it's still unquestionably Eurocentric, especially after the first book. For example, well over half of the second book is specifically about Europe, the "Age of Exploration" is almost entirely from a European perspective, Bauer seems to use European sources when writing about a lot of Asia (for example, the only view of medieval Central Asia we ever see is from Marco Polo's eyes), etc. It is impossible for any author to write any kind of history without at least some of her biases coming through and SOTW is no different.
It's interesting that most of the complaints about this series are about specific chapters or time periods- Muslims complain about the chapter on Muhammad, Catholics are uncomfortable with the chapter on the Reformation, lots of people complain about the fourth book, etc. In my mind this is because people see the weaknesses in SOTW when it's discussing the history they are most familiar with. The complaints about the fourth book (1850-1991) are largely a result of parents' familiarity with modern history. Muslims are going to write the history of Muhammad differently than someone who isn't as sympathetic towards Islam.* But the point is that these differences in interpretation are throughout the entire series, but few parents (myself included) can pick them all out because few parents are well versed in every aspect of world history.
Don't get me wrong. I use and will continue to use these books. This just isn't the definitive version of children's history that it is sometimes touted to be (and any parent who relies on these books only for their knowledge of world history is not doing themselves a favor). What I'd really love to see is a series like this written by a wider variety of authors. Authors who have specific expertise in a give area and who also are good at writing for children. That wouldn't be easy to produce, but I'd buy it if it were out there.
*I think the Muslim complaints are valid. Bauer unquestionably tries to be unbiased, but we didn't use the chapters on Islam at all. Instead, I used a few of my own books to discuss the Muhammad and the founding of Islam from a more Muslim point of view. I also find that I am often correcting what we listen to on the CDs (when I read out loud, I do a lot of rewording in every single chapter). But I think this is useful because I want my children to understand that history isn't an exact science. There is no history book I could buy that I would agree with on every point.