This answer, to be terribly honest, will be incredibly United States-centric, because I think both of these books should be read in every single United States history class being taught in this nation.
One of the issues with history is that we are rarely given straight facts; we're usually given a few facts in every story and then an incredible dancing interpretation based on the current ruling politics in the nation or the textbook industry. This means that schoolchildren in this country learn so many completely untrue things about history that the first year of any history major's college career is spent breaking down all those lies and teaching them that, first and foremost, about 75% of their history textbook is either a lie or an elaborate fabricated interpretation of a truth.
DISCLAIMER: Some people may consider a discussion on the faults of the textbook industry in America overly political on my part, since I run this blog almost entirely as a non-political thing. I am making this small exemption here because I feel these books are just that important. For your comfort, however, I will provide a jump.
Click 'Read More' to see my answer.
So I think every high-school kid in America should have to read two books:
Lies My Teacher Told Me by James W. Loewen and A Peoples' History of the United States by Howard Zinn.
Lies My Teacher Told Me is a very breezy, quick read, a short discussion on the textbook problem in this country and then somewhat of a speed-through, running through many of the things the textbooks either do not say or outright are dishonest about.
The discussion on the dishonesty of the textbook industry is an important one. It's not that textbooks tend to swing left or right, but rather that they swing at all. Rather than presenting the facts of the matter and of historical events as they happened, often important figures who are not considered "noteworthy" by the writers or publishers are left out entirely, important documents are rarely quoted in their entirety but instead 'paraphrased', meaning that even if kids get to read about the document, they still get an individual interpretation of it rather than the real thing, and the biggest problem of all: American history textbooks are explicitly written to create obedient citizens rather than to inform about history.
Reconstruction is rarely written about as it actually happened, for instance, instead falling prey to an early-20th-century nostalgia about the antebellum and post-war South that isn't accurate in the slightest. In recent news, the Texas Board of Education voted to make many incredibly political changes to what textbooks they accept: and Texas is where most of the country's textbooks are printed, and the way that Texas votes changes our history books all over the nation.
Loewen's book is an easy read for high schoolers, and if Zinn's book had to be left out, I would feel at least a little better, because we'd know that while the students must read the interpretations of textbooks writers, they could also get another side to history's stories. Another great upside is that Loewen is not one of those who falls prey to blaming the teachers, who must work with what materials they are given and often find themselves having to text to each standardized test instead of being able to analyze and really debate the mythology the textbooks are giving students. Too many books blame teachers for not doing enough or occasionally for doing too much.
If I could only pick one, I would pick Loewen's book.
A People's History of the United States by Howard Zinn may be a little more polarizing, as Zinn is a Marxist and is writing somewhat from what perspective. The book is excellent perhaps because of this, because this is a history of the country that is not written from the point of view of the robber barons, the ultra-rich, the politically in-charge, the ones who had it easy, those who have spent the entire history of this nation tweaking historical events to fit their mental image of how things should have been.
This is a book written from the point of view of the bulk of American citizenry; the people, those whose voices are consistently pressed down; the people who had to fight for every inch of rights the wealthy landowners refused to give them. The Civil Rights movement is covered here in a single chapter in more depth than a hundred high-school textbooks have ever been able to give it.
Zinn writes in a timeline; he starts in the famous 1492 in which Christopher Columbus stumbled onto an already-inhabited land and declared he had 'discovered' it, and goes piece by piece through the history of this nation, going as far as the turn of the 21st century, though not quite up to the moment of today.
One of the global criticisms of the United States is that our children and young adults seem so completely unaware of our own history, and this criticism is very, very true; it is because we don't teach our children history, we teach them a legend and a set of myths we have created using a couple of true facts and a whole lot of shiny shiny tinsel meant to distract us from the holes.
These two books would go a long way towards fixing that great problem in our schools, in that we would have the textbook and have these two books as well, and kids could read the legend and the myth and then read more facts and a different point of view. This would lead to high-school age kids whose ability to think critically and analyze their own histories would be much greater, more developed.
There is no way that teaching kids to think critically is bad... unless the idea is to create people who never question the story they're fed.
So there you go; these are two books I think every human being raised in the United States should have to read before they are seniors in high school, before they go to college or out into the world. Learning to anaylze history and its different shades and shadows alone would go a long way towards the ability to critically analyze much of their own lives.