I feel that two things need to be accepted if this book is going to be appreciated.
Roberts one-way-or-another justifies the emphasis that he places on Europe (and especially Western Europe) and (later) on America in account of the fact that these areas are largely influential in the world today. In this sense, it is more a history of the modern world - and of events that brought this about - rather than of the world as it may have been at any selected time in history. Given this logic, areas like China, for example, tend to receive attention more proportional to Roberts' assumptions on their place in the world at the time of writing, rather than in respect to how powerful and influential they may once have been (or may soon become).
Accordingly, this history starts off more-or-less in the traditional way, with much emphasis being placed on the early Middle Eastern / Mediterranean civilisations (the Sumerians, the Egyptians, the Greeks, etc). It then progresses comfortably to the rise and fall of Rome (and the Greco-Roman Empire) and then to the tumultuous rise of (especially Western) Europe to world supremacy. As we know, this then passes on to America and (for a while) Russia.
All the other main players, such as Japan, China, India, and the Ottoman Empire (to name only a handful) receive their due chapters (often with much emphasis on how they affected or otherwise failed to affect Europe). Then of course such civilisations as those once belonging to the Americas get their coverage partly because we've heard of them, partly because it's important to see how Western civilisations swept them away, and partly (I venture to say) because without the Americas the book would hardly seem geographically balanced.
What I am getting at here is that this book might disappoint some people who want for a more balanced perspective on history, but it shouldn't significantly bother anyone who is happy to read the chain of events as outlined above. As I have already touched upon, some justification can be found in the fact that Roberts is really more interested in giving us a history as far as it has shaped today's world. Another thing to bear in mind is that it is merely a one volume book, and as such much of these limitations are quite unavoidable. This is the first thing that a reader must come to accept if he or she is going to enjoy this book (and readers who are looking for a more balanced and thorough account need to appreciate that they will ultimately have to read a great many related books). After all, there is much history to be understood from this book, even if it cannot hope to fit the whole history of the world so neatly into only one volume.
The other thing to accept or appreciate is more a matter of the book's register. For example, it may help if the reader already has some general historical knowledge; it is very much a book for people who are already fascinated by history. (There are much more entertaining reads for those who are relatively new to the subject. Try something by Giles Milton, or read something more specific - say, about WWII, or any other particular history that interests you.) In other words, I doubt this is a book to inspire in the uninitiated a new found love for historical literature, but if you already have this love then this book will do much to further your interest and consolidate your knowledge.
By way of another example, I am at the moment two-thirds of the way through reading 'The Penguin History of Europe', by J.M. Roberts - I have already read many similar histories (such as 'Europe: A History', by Norman Davies) - and I find Roberts' style to be very similar in both books. It is in no way nearly as balanced or compulsive as other reads (Davies' book is brilliant for this), but it is thorough, educational, and mostly enjoyable, and it keeps me turning the pages. However, it may say something to add that I have read perhaps seven or eight other books since starting on this one if only to keep it light, and so neither reads are easy.
Overall, 'The New Penguin History of the World' is a thoroughly good book. It is mostly interesting, always educational, and it pretty much accomplishes what it sets out to do. If you can accept the near-inevitable Western emphasis on this book, and if you are already something of a history buff, then I am sure that you will fully enjoy this read. I may have found it a challenge - sometimes getting through a chapter could be nearly overwhelming - but this reflects more on the depth of the work than on the style in which it is written. It is much to say for the book that despite the density of the thing it kept me happily turning the pages for weeks on end.