Fascinating topic, been thinking about it all day. Two I was thinking of were Children of Men and Saving Private Ryan.
Children of Men : one of the major things happening right now is the decrease of fertility in Europe and North America, + refugee crisis which might become a major element specific to the 21st century. Also it's very good, so that might be wishful thinking.
Saving Private Ryan : less confident about this one, but certainly THE thing defining the 20th century are the world wars (and the cold war, but I think the world wars will be the n°1 thing), so when Chuck started talking about a film depicting a historical event in a way that makes the film overshadow the event... that D-Day sequence might be it for future generations. For us, D-Day is a very concrete thing because our parents/grandparents were alive for it, but I can imagine future history teachers using Saving Private Ryan to show what war was like in the 20th century.