Cloverfield (2008)

Cloverfield follows five New Yorkers from the perspective of a hand-held video camera. The movie is exactly the length of a DV Tape and a sub-plot is established by showing bits and pieces of video previously recorded on the tape that is being recorded over. The movie starts as a monster of unknown origin destroys a building. As they go to investigate, parts of the building and the head of the Statue of Liberty come raining down. The movie follows their adventure trying to escape and save a friend, a love interest of the main character.