The Japanese movie that stands out the most to me is "Nobody Knows". I found two trailers for it on youtube and neither come close to doing it justice. It's about four children with a single mother who is struggling to get by. The mother meets a man and as the dating process continues, the children see less and less of their mother. And if you want any more of the story, you're going to have to watch the movie!
I'm glad this topic has come up because I see this movie is not on my favourite movies of all time list, and it deserves to be.
The naturalistic film-making style of the children-only scenes was a good decision, with (12 year old) Yuya Yagira anchoring the movie amazingly well portraying the elder son.
The fact that the movie had some basis on a true incident really added to the overall impact for me.
And yes, Departures and Like Father Like Son are both mandatory viewing as well, IMO.