One of the films I've never had time to watch is "Monsters", a 2010 film that explores the issue of mankind having to deal with extraterrestrials as co-inhabitants in Central and North America.
I started out "just watching five minutes" and ended up being totally engrossed in this film. it is just outstanding and I highly recommend it.
This film utilized $15K in film equipment (mostly consumer-class video cameras) and cost a whole $500K to make.
If you're expecting "Independence Day", "War of the Worlds" or some sort of Godzilla movie you'll be disappointed. If you want to delve deeper into human behavior then you'll likely find this film to be most enjoyable. The soundtrack by Jon Hopkins is also very good.