I've had The Rise and Fall of the Third Reich by William Shirer on my bookshelf for years yet never took the time to pick it up, but I've been told and read that it was somewhat biased against Germany.
Read it. It is an excellent book. It is not biased against Germany--in fact, it praises many Germans quite highly, especially those who opposed Hitler, and also the vast majority of the regular Germans who bore the bombings and horrors with exemplery patience (his words, by the way). What he does have is white-hot hatered of NAZISM--which is something quite different.
The book is biased, though, in the sense of this being a personal work by a journalist, not a research tome by a professional historian. So Schirer tends to be light on the documentation (relatively speaking, of course--he DOES have a lot of footnotes and a huge bibliography, but less than you would expect for a work that covers all of the Nazi era), and sometimes sacrifices details and accuracy to tell a more compelling story.
Nevertheless, he is a fascinating writer, and his book--while somewhat outdated--has, by and large, survived a lot of criticism and later research. If not always 100% accurate, it is still very nearly true in every essential point.
So what's the best book out there about WW2?
It depends. An excellent one is Bollock's HITER: A STUDY IN TYRANNY, which is also somewhat shorter than the others below. Perhaps the most outstanding single book is HITLER by Joachim Fest, while the most up-to-date and comprehensive book is the two volume HITLER, 1933-1938: HUBRIS, and HITLER, 1939-!945: NEMESIS by Ian Kershaw.
Perhaps also useful is what books to avoid, which includes many quite famous ones. Avoid all books by David Irving, a holocaust denier with a Hitler fetish. Robert Payne's THE LIFE AND DEATH OF ADOLF HITLER runs across Hitler's life with a dashing disregard for the truth, while Albert Speer's INSIDE THE THIRD REICH is simply the usual apologetics of the ex-war criminal, not a word of which can be trusted.