As you probably know, the conceit of this film is that it is meant to be found footage, recorded on a camcorder by the characters in the film. It starts with them being at a going-away party for one of the characters, but then the city they are in (New York, naturally) is attacked by a giant monster. The rest of the film features a lot of people running around going "Oh Jesus, what was that?" as they try to escape Manhattan or rescue friends or whatever it is that people do in this kind of film. I found it very involving, with the human scale treatment of something as outlandish as a monster-smashes-city setup being quite affecting. The original Japanese Godzilla film does something similar with one scene in a hospital for people who have been injured by the eponymous monster*. Cloverfield, however, eschews the Generals-explaining-plot scenes you usually get in this kind of thing, and is more effective for it.
I did hear that some people found the characters in the film annoying, but I found them sufficiently engaging that I started inwardly grumbling about horror film tropes that require them to be killed off one by one. The film does not in fact really go for that… I'm not saying they are all still alive when the film ends, but it does not kill one off every ten minutes when they move to a new location, disaster-film style. As a form of plotting I reckon this works well, as does having the camera be pointing in the wrong direction at key points in the film (as in, I still don't really get what happened when they tried to cross the bridge, but I know it was scary).
Favourite scary moment in the film: the "why are all the rats running in that direction?" bit. Or the "I don't feel well" bit.
Some people liked Cloverfield. Other people did not.
*I am not the first person in the world to mention this.