Well, after a very lengthy Monday post, I ended up missing a few days...and now here's a short list of recommendations.
This list is inspired by the current run of Matthew Porterfield's I Used to Be Darker at Sundance Cinemas, and my recent viewing (finally) of the original The Wicker Man (unfortunately I haven't seen the restored print of The Wicker Man that has been circulating in theaters).
This is a list of films that feature singing but are not musicals, properly speaking, or are very unconventional musicals. I Used to Be Darker is not streaming yet (but I recommend putting it in your queue at GoWatchIt), so I'm adding the film that it most reminded me of, Once (2006). Okay, Once has been easily translated into a Broadway musical, but I'm not sure if it is a film musical.
What all these films share is that they engender the unique exhilaration of simply watching someone sing, especially when you're not expecting it. I think elaborating on that might ruin the experience, if you're not already familiar with these films. This list certainly is not exhaustive (I considered putting Nashville and Magnolia on the list...oh, I guess I just did), so any additional recommendations on this theme are welcome in the comments section.
Posters and Synopses from The Movie Database
The Wicker Man (Robin Hardy, UK, 1973, 89 minutes)
Police sergeant Neil Howie is called to an island village in search of a missing girl whom the locals claim never existed. Stranger still, however, are the rituals that take place there.
Once (John Carney, Ireland, 2006, 85 minutes)
The Guy is a Dublin guitarist/singer-songwriter who makes a living by fixing vacuum cleaners in his Dad's Hoover repair shop by day, and singing and playing for money on the Dublin streets by night. The Girl is a Czech who plays piano when she gets a chance, and does odd jobs by day and takes care of her mom and her daughter by night.
La France (Serge Bozon, France, 2007, 102 minutes)
During the First World War, Camille (Sylvie Testud), a young woman whose husband is away fighting at the front, receives a short letter of break-up from him. Distraught, she decides to go to join him, but is driven back by the rule of the time which forbids women to move around alone. She has no other recourse than to dress herself up as a man so as to be able to take to the road on foot. As she lives near the Western Front she hooks up with a passing group of French soldiers without too much trouble. But there's something a bit odd about these stragglers, and it's not just their habit of bursting into song at every opportunity.
The American Astronaut (Cory McAbee, USA, 2001, 91 minutes)
Samual Curtis's first mission in this bizarre science fiction musical comedy requires him to take a cat to a saloon on an asteroid. There, he meets his former dance partner (the Blueberry Pirate) and collects his payment: a device capable of producing a Real Live Girl. Including music by alternative rock group The Billy Nayer Show, this film began life as a live show with a loyal following.
Stingray Sam (Cory McAbee, USA, 2009, 61 minutes)
A dangerous mission reunites Stingray Sam with his long lost accomplice, The Quasar Kid. Follow these two space-convicts as they earn their freedom in exchange for the rescue of a young girl who is being held captive by the genetically designed figurehead of a very wealthy planet.
I Used to Be Darker (Matthew Porterfield, USA, 2013, 90 minutes)
When Taryn, a Northern Irish runaway, finds herself in trouble in Ocean City, MD, she seeks refuge with her aunt and uncle in Baltimore. But Kim and Bill have problems of their own: they’re trying to handle the end of their marriage gracefully for the sake of their daughter Abby, just home from her first year of college. A story of family revelations, people finding each other and letting each other go, looking for love where they’ve found it before and, when that doesn’t work, figuring out where they might find it next.