It sounds like what you are looking for, is what is generally called "popular history": easy to read, not academic, utilizes more personal touches. I would caution that they are not always the best sources of information, or completely accurate.
For the Second World War period, you may want to consult Anthony Beevor. His books "Stalingrad" and "Berlin: the downfall" were particularly highlight praised although not without controversy. They are easy and fast reads that focus on personal accounts about as much as telling the story. His later work "D-Day" brought various generally obscure things to light, such as Allied war crimes, but on the whole - imo - it is largely utter tosh and inaccurate. His early work on Crete is highly praised, although I found it a dry read.
Charles Mann's "1493: Uncovering the New World Columbus Created" is another popular history that follows the author's travels around the world looking at the world Columbus "created". For me, having just finished studying the rise of global empires at university, there was very little in the way of new information in it and I only bought it to read on the plane. It goes on to long in places, but other sections are fascinating and on the whole the book is rather enlightening. I have not read it, but his earlier work "1491: New Revelations of the Americas Before Columbus" also received high praise.
One of my favorite books is "After Tamerlane: The Rise and Fall of Global Empires, 1400-2000" by John Darwin. It is pretty academic and a serious study of empires during the period, but it is very accessible and utterly fascinating.
As soon as you said no school text books, the following popped to mind: "
The Long European Reformation: Religion, Political Conflict and the Search for Conformity, 1350-1750" I actually fell asleep reading this one ... several times! avoid :P
"I would recommend most of the books of Stephen Ambrose for non-fiction ... His writing style is much more like a novel or story-telling than a history textbook ..."
I doubt that some historians would argue that his writing style is that way because they are fiction. Ambrose is a very much criticized historian, although his books on Normandy were pretty good reads. Just don't take them as the final say on anything.