I first found history interesting and exciting about the time I started playing Dungeons & Dragons and similar fantasy role-playing games. While the spotlight in those games shines on the fantastic (e.g. dragons and such), there is still a surprising amount of history that can be learned. As you might expect, the historical period that commanded my attention was the medieval, complete with feudal lords, knights, men-at-arms, et cetera. I remember being fascinated with David Macaulay's Castle, books about weapons and armor, books on the crusades, sections of H.G. Well's The Outline of History, and similar works. I also loved books about ancient Egypt and about Vikings. Later, I also started playing role-playing games and tactical board games (i.e. war games) based on World War II, so I expanded my historical interest into those areas as well.
As I grew older, my interest in history grew deeper and broader. A great deal of my reading, these days, is history. I still enjoy books on the crusades, vikings, and WWII, and have recently been reading books about the near-east in the bronze age (including Egypt, but not focusing there, exclusively). I also enjoyed reading about the Civil War, and about the First World War (and the period immediately before it). Currently, my interest is focused on the late bronze age in Canaan/the Levant, Anatolia, and North Africa. I want to read more about ancient Greece and Rome, and also about the Byzantine empire. Another big gap, for me, is the Napoleonic wars and that period.
This list doesn't include every history book I've read, only ones I really enjoyed. An asterisk indicates a book which I haven't read, but is on my "to be read" list because I like the author or because it is highly recommended.
Broad Histories
*Birth of the Modern by Paul Johnson
*A History of the American People by Paul Johnson
*A History of the Jews by Paul Johnson
*From Dawn to Decadence by Jaques Barzun
Bronze Age and Imperial Rome
Life in Biblical Israel by King and Stager
The Collapse of the Bronze Age by Manuel Robbins
The End of the Bronze Age by Robert Drew
Saint Peter by Michael Grant
*History of Rome by Michael Grant
*The Landmark Thucydides by Robert Strassler
The Western Way of War by Victor Davis Hanson
Dark Ages, Medieval, Renaissance
A History of the Vikings by Gwyn Jones
Oxford History of the Vikings by Peter Sawyer (editor)
The Vikings and America by Erik Wahlgren
Life in a Medieval Village by Frances Gies
A Concise History of the Crusades by Thomas Madden
The Crusades: The World's Debate by Hilaire Belloc
*The Sword of the Prophet by Srdja and Serge Trifkovic
*Bible and Sword by Barbara Tuchman
A World Lit Only by Fire by William Manchester
A Distant Mirror by Barbara Tuchman
*Joan of Arc: Her Story by Régine Pernoud
*Joan of Arc: By Herself and Her Witness by Régine Pernoud
*The Crusaders: The Struggle for the Holy Land by Régine Pernoud
*Those Terrible Middle Ages: Debunking the Myths by Régine Pernoud
Early American History
John Adams by David McCullough
Common Sense by Thomas Paine
Our Sacred Honor by William Bennett
The Federalist Papers by Alexander Hamilton
Democracy in America by Alexis de Tocqueville
*The Glorious Cause: The American Revolution by Robert Middlekauff
*1812: The War That Forged a Nation by Walter Borneman
The Civil War
The Civil War: A Narrative, Vol. 1 by Shelby Foote
*The Civil War: A Narrative, Vol. 2 by Shelby Foote
*The Civil War: A Narrative, Vol. 3 by Shelby Foote
*Stars in Their Courses by Shelby Foote
World War I
The Proud Tower by Barbara Tuchman
The Guns of August by Barbara Tuchman
The First World War by John Keegan
The Zimmermann Telegram by Barbara Tuchman
*The Arms of Krupp by William Manchester
World War II
Goodbye, Darkness by William Manchester
The Second World War by John Keegan
The Rise and Fall of the Third Reich by William Shirer