Babel (2006)
Alejandro González Iñárritu is also the director of 2003 movie '21 Grams' (which I could not bring myself to watch yet, even if I hear good things about it). I liked Babel. It is clean and it has great pacing. I liked most of all the way the stories move in the plot, the fact that even if loosely connected the three stories are given different weight. There is some sort of a central story (with Brad Pitt in it) but I watched with even more interest the story from Japan which is almost not connected by solid links to the rest but mainly by a whole atmosphere. The characters in all the story share something else than things and family or social relationships.
The moral of the whole thing has been criticised to be a little too obvious but the movie is done so well that I couldn't care less. One issue that can be discussed is why would you cast known actors in a movie where they can hinder the message if the moral is supposed to be the one stated above. Surely, I can perfectly imagine this film completely with unknown actors. On the other hand, one can say that this is exactly the point: (film)stars are connected to the rest in the same way. And 'American citizens' are in any case a type of star nowadays so it might be that Americans as a people are connected to Muslims and Japanese. In any case, this movie is much more about the whole world then about particular actors.
When you watch this one also listen to its music. Gustavo Santaolalla wrote the music as well for 21 Grams and for Amores perros (2000) and this would probably be another good reason to check out these movies.