An excellent book that covers all of history and is used at a university level is A History of World Societies which is written by several scholars. It is quite a read but it is richly illustrated and covers both Europe as well as the rest of the world.

If you want asian centric try out; "ReOrient" by Andre Gunder Frank, its certainly an interesting perspective.

"Imagined Communities" by Benedict Anderson is certainly a world-history, focusing mostly as the rise of the modern state; he begins the book in Europe, but as his experience in mostly in South East Asia the book covers a great deal of that area in order to describe the creation of global norms.

"Something New Under the Sun" by J.R. McNeil is a good world history for changes in energy regimes- the movement from burning natural products to coal to oil and beyond. Its an environmental history that concerns itself with global phenomena and not just Euro-American perspectives.

The textbook we use is "Traditions and Encounters" is goes all over the place; but I find textbooks are not particularly enlightening reads if you are just doing it for fun. Its pretty sensitive to covering the entire globe and not just being centered on Europe; as well as addressing women's history and voices, especially with the newer editions.

Those are the books that just spring to mind; so I guess it kind of depends on what sort of world history book you are looking for... academic, casual, textbook, and what time period(s) you are interested in reading about.

You definitely can't go wrong with Harvard's new "History of the World" series, which has had two publications thus far: Global Interdependence: the World After 1945 and A World Connecting, 1870-1945. They're each about 900-1000 pages, with several book length essays on various subjects. They're both absolutely great reads.

You may also like Jurgen Osterhammel's The Transformation of the World: A Global History of the Nineteenth Century

For Islamic Societies, which obviously covers much of the world, not to mention interactions of non-muslim societies with "Islamdom," Marshall Hodgson's three volume "The Venture of Islam" is excellent.