Do you have a more specific interest in 20th century history? It's going to be hard to list three books that can give a comprehensive overview of the century, especially because there is such a fundamental shift in global history after WWI and, even more significantly, after WWII. Even so, by far the most comprehensive books are the two most recent volumes in the new Oxford History of the World series:

• A World Connecting, 1870-1945, edited by Emily Rosenberg and Akira Iriye

• Global Interdependence: The World After 1945, edited by Akira Iriye and Jurgen Osterhammel.

You're not going to get more well-written histories of the 20th century that are so comprehensive. At the same time, I doubt you'll want to read roughly 2000 pages over the holidays. Still, I can't not mention these books when someone is looking for something on the history of the 20th century.

Here are three more accessible books that, while more specific in subject, touch on much more general themes of 20th century history.

• Daniel Rodgers, Atlantic Crossings: Social Politics in a Progressive Age

• Odd Arne Westad, The Global Cold War: Third World Interventions and the Making of Our Times

• Jeremi Suri, Power and Protest: Global Revolution and the Rise of Detente, or Mark Kurlansky's 1968: The Year that Rocked the World

If you'd rather read general overviews of the 20th century, here are a couple of good ones:

• J.M. Roberts, 20th Century: The History of the World, 1901-2000

• Eric Hobsbawm, Age of Extremes: A History of the World 1914-1991

I wouldn't suggest just reading overviews though, as they will most likely get repetitive.

I'll start by echoing /u/gent2012's comments that this is a tall-order given the scope and scale of the 20th century, and any specific interests would help narrow it down enormously.

The addition to /u/gent2012's suggestions that I would make is Martin Gilbert's History of the Twentieth Century Series, which happens to be three volumes. See vol: I, II, III. They are generally well regarded and personally I find Gilbert's style quite readable. If you're looking for something fairly general, they might be a good place to start.

Other than that, Mark Mazower's Dark Continent: Europe's 20th Century is another easy recommendation which covers the time period, albeit more geographically focused.

Perhaps give the AskHistorians book list a browse and see if anything catches your eye.

how about

barbara tuchman: the proud tower OR the guns of august

frederik logevall: embers of war

daniel yergin: the prize