Mexico (the "crack" generation)
In Search of Klingsor by Jorge Volpi

Amphitryon by Ignacio Padilla

Diorama by Vicente Herrasti
The Host by Guadalupe Nettel

Peru
Lost City Radio by Daniel Alarcón
Red April by Santiago Roncagliolo

The Blue Hour by Alonso Cueto
Don't Tell Anyone by Jaime Bayly
Etiqueta Negra magazine (narrative journalism; only available in Spanish)

Chile (the McOndo literary movement)
Bad Vibes by Alberto Fuguet
The Private Lives of Trees by Alejandro Zambra

Daniel Alarcón (Photo credit: Kanaka Menehune)

Colombia
The Secret History of Costaguana by Juan Gabriel Vásquez

Brazil
Mastroianni Day by João Paulo Cuenca
Symphony in White by Adriana Lisboa

Argentina
The Year of the Desert by Pedro Mairal
Traveller of the Century by Andrés Neuman

Puerto Rico
Yo-Yo Boing! by Giannina Braschi

Fiona Sampson's poetry recommendations

César Vallejo: The Complete Poetry ed Clayton Eshleman (University of California Press)
The Essential Neruda ed. Mark Eisner (Bloodaxe)
The Collected Poems of Octavio Paz, ed Eliot Wienberger (New Directions)
Against Heaven by Dulce María Loynaz trans. James O'Connor (Carcanet)
Migrations by Gloria Gervitz trans Mark Schafer (Shearsman)
Anima by José Kozer trans Peter Boyle (Shearsman)
The Whole Island: Six Decades of Cuban Poetry ed Mark Weiss (University of California Press)

World literature tour recommendations

Chile
Argentina
Colombia

via Guardian Books podcast: Latin American novels and poetry