Training Day (2001)
Kill Bill (2003)
Children of Men (2006)
Life of Pi (2012)
Birdman (2014)
(Honorable mentions: Whiplash, A Waking Life, Apocalypto, Lost In Translation, Memento)
1)In the mood for love
2)Spirited Away
3)Yi Yi
4)The Tree of Life
5) The Turin Horse
Easy as pie. Of all the films I've seen in my lifetime, I consider 19 to be classics, out of the 19 only 6 are from the 2000-present, so all I had to do was leave out one.
This list is on point.....I would take off Life of Pi and put in Inception on my list though. But really I'd take your list in a heartbeat