A History of Slovakia: The Struggle for Survival by Stanislav Kirschbaum -- The most comprehensive English-language history of Slovakia, covering the long arc from the Great Moravian Empire to independence in 1993. It explains why Slovakia is not simply "the other half of Czechoslovakia."
The Czech and Slovak Republics (Lonely Planet or Rough Guide) -- The most practical English-language travel guides available. Both cover Slovakia thoroughly, with good sections on the Tatras, Bratislava, and eastern Slovakia.
Katarina by Kathryn Winter -- A memoir set in wartime Slovakia, based on the author's childhood. It offers an intimate portrait of Slovak life during one of its most turbulent periods.
Rivers of Babylon by Peter Pist'anek -- A darkly comic novel about the chaos of post-communist Bratislava, following a dodgy parking attendant who builds a criminal empire. Not available in every language, but if you can find it in English, it captures the wild energy of the 1990s transition.