Movies:
Girl - a movie from Japan that features a single mother trying to raise her son. She is looked down upon by her peers because they believe her son isn't getting the correct "role model" as he's growing up without a father-figure around.
Himizu - A son who lives with his more often than not drunk mother. His father comes home occasionally to bum money off the mom and throw his fists around a bit. Shows the psychological damage this has on the son.
Dramas:
Down With Love - a Taiwanese drama about 2 children who've lost their parents and are taken in by their uncle. Their uncle doesn't really know how nor want to deal with children, though, so he hires a nanny to take care of them. The relationship between the uncle and children gradually becomes warmer and more family-like
Heaven's Mandate - a Korean saeguk featuring a single father and his sickly daughter. The father is a physician in the Royal Court, from which he gets the medicines to treat his daughter. They're separated for some time, however, and a lot of the story is devoted to the father finding a way to get back to his daughter.
Brother Beat - a Japanese drama about a single mother and her three grown sons. The mother has an unconventional approach to raising her sons. Mostly a light and fluffy drama
Mother - a Japanese drama about an abused daughter and her teacher who decides to raise the girl herself and take her out of that situation. Also focuses on the teacher's relationship with her mother, who also had to raise her daughter on her own.
My Prince - the Mainland Chinese version of Brother Beat, about a single mother and her four grown sons.