Lists!
Indie Wire
10. "Gloria"
9. "Upstream Color"
8. "Computer Chess"
7. "Inside Llewyn Davis"
6. "Museum Hours"
5. "Blue Is the Warmest Color"
4. "The Act of Killing"
3. "Before Midnight"
2. "Leviathan"
1. "12 Years a Slave"

Sight & Sound
1. The Act of Killing (dir. Joshua Oppenheimer)
2. Gravity (dir. Alfonso Cuaron)
3. Blue is the Warmest Colour (dir. Abdellatif Kechiche)
4. The Great Beauty (dir. Paolo Sorrentino?)
5. Frances Ha (dir. Noah Baumbach)
6. A Touch of Sin (dir. Jia Zhang Ke)
7. Upstream Color (dir. Shane Carruth)
8. The Selfish Giant (dir. Clio Barnard)
9. Norte, the End of History (dir. Lav Diaz)
9. Stranger by the Lake (dir. Alain Guiraudie)

Cahiers du Cinema
1. Stranger by the Lake (dir. Alain Guiraudie)
2. Spring Breakers (dir. Harmony Korine)
3. Blue Is the Warmest Colour (dir. Abdellatif Kechiche)
4. Gravity (dir. Alfonso Cuaron)
5. A Touch of Sin (dir. Jia Zhang Ke)
6. Lincoln (dir. Steven Spielberg)
7. Jealousy (dir. Philippe Garrel)
8. Nobody’s Daughter Haewon (dir. Hong Sang-soo)
9. You and the Night (dir. Yann Gonzalez)
10. La Bataille de Solferino (dir. Justine Triet)

Empire
...
5. Lincoln
4. Mud
3. Rush
2. Captain Philips
1. Gravity
http://www.empireonline.com/features/films-of-the-year-2013

TIME
10. The Hobbit: The Desolation of Smaug
9. 12 Years a Slave
8. The Act of Killing
7. Frozen
6. Fast & Furious 6
5. The Grandmaster
4. her
3. American Hustle
2. The Great Beauty / La grande bellezza
1. Gravity
http://entertainment.time.com/2013/12/04/arts-and-entertainment/