I can't lay claim that these are necessarily the greatest works of the century so far, but in looking at my Goodreads, these were the 21st century works I gave 5 stars to. I really enjoyed all of them for what that's worth. The Novels are the most diverse, but I feel that in the US, Novels and Novellas get translated more often than the other genres.
Novels
(2000) Vargas Llosa, Mario The Feast of the Goat (Peru)
(2000) Smith, Zadie White Teeth (UK)
(2002) Murakami, Haruki Kafka on the Shore (Japan)
(2004) Thiong’o, Ngugi wa Wizard of the Crow (Kenya)
(2005) Ishiguro, Kazuo Never Let Me Go (UK)
(2006) McCarthy, Cormac The Road (USA)
(2006) Yan, Mo Life and Death Are Wearing Me Out (China)
(2007) Han, Kang The Vegetarian (South Korea)
(2014) Fresán, Rodrigo The Invented Part (Argentina)
(2014) Tawada, Yoko The Emissary (Japan)
Short Stories
(2003) Munro, Alice Runaway (Canada)
(2013) Saunders, George Tenth of December (USA)
Plays
(2001) Parks, Suzan-Lori Topdog/Underdog (USA)
(2003) Ruhl, Sarah Eurydice (USA)
(2003) McDonagh, Martin The Pillowman (UK)
(2009) Nottage, Lynn Ruined (USA)
(2014) Baker, Annie The Flick (USA)
Memoir
(2005) Didion, Joan The Year of Magical Thinking (USA)
Poetry
(2007) Freitas, Angelica Rilke Shake (Brazil)
(2010) Hayes, Terrance Lighthead (USA)
(2012) Gelman, Juan Dark Times Filled With Light (Argentina)
(2014) Rankine, Claudia Citizen: An American Lyric (USA)
(2018) Limon, Ada The Carrying (USA)
(2018) Nezhukumatathil, Aimee Oceanic (USA)
(2018) Zagajewski, Adam Asymmetry (Poland)
Essays
(2014) Gay, Roxane Bad Feminist (USA)
(2015) Tevis, Joni The World is On Fire: Scrap, Treasure, and Songs of the Apocalypse (USA)
(2016) Luiselli, Valeria Tell Me How It Ends: An Essay in 40 Questions (Mexico)
(2019) Tolentino, Jia Trick Mirror: Reflections (USA)