Fiction
The Millennium Trilogy by Stieg Larsson — The Girl with the Dragon Tattoo and its sequels put Stockholm (and the Swedish crime thriller genre) on the international map. Dark, gripping, and surprisingly good on Swedish social texture.
The 100-Year-Old Man Who Climbed Out the Window and Disappeared by Jonas Jonasson — A lighter choice: absurdist comedy that sweeps through 20th-century history. Fun for long train journeys north.
Pippi Longstocking by Astrid Lindgren — If you're travelling with kids, or just want to understand Sweden's beloved outsider spirit, Lindgren is essential. Vimmerby in Småland, where she grew up, is now a major attraction.
August is a Wicked Month by Edna O'Brien — Not Swedish, but set partly in Sweden and captures a particular mood of Nordic summer.
Non-Fiction and Background
The Almost Nearly Perfect People by Michael Booth — An irreverent British journalist's examination of Scandinavian society. Funny and sharp, with good chapters on Sweden's relationship with its Nordic neighbours.
Sweden: The Nation's History by Franklin D. Scott — Dry but thorough academic history if you want proper context before visiting.
The Nordic Secret by Lene Rachel Andersen and Tomas Björkman — An argument about how Nordic societies developed their particular political cultures. Dense but interesting for those who want to understand the modern welfare state.
Crime Fiction Set in Sweden
Henning Mankell's Kurt Wallander novels are set in and around Ystad in Skåne — worth reading if you're heading to southern Sweden. Camilla Läckberg sets her thrillers in Fjällbacka on the Bohuslän coast.