Saw it, thought it was fantastic (although the thirteen-year-olds scattered hither and about annoyed the piss out of me). Of course, I'm always a little wide-eyed when I see stuff on the big screen...
Aside from the relatively stale framing device (this tape is recovered footage) -- that I honestly shouldn't complain about, since all framing devices are stale by this point, I thought it was a return to the most fundamental aspect of storytelling, personal experience.
First-person cinema is very rare. The problem with first-person stuff is that you generally know that the storyteller will survive, except if the writer uses a cheap trick. Here there are no cheap tricks, and the storyteller is no safer than anyone else.
It's also similar to second-person literature in that the audience is placed in the story but manipulated, forced to conform to behaviors they would not follow in order to maintain the story's integrity. Here again, the audience is passive, being manipulated by the storyteller's environment, and yet there's never the sense of being manipulated in order to further the plot. The characters' motivations play out to their logical ends and there are no fortunate coincidences or feelings that the plot is stretched to the breaking point.
Despite the framing device, there's no lack of immediacy. Some critics have criticized the acting and scripting as relatively lukewarm, but I have to say that it seemed intense and real to me throughout. Of course, some critics have also said the film was "cashing in on 9/11," which is precisely the idiotic protectionism that a transgressive like me loathes above all other pretensions (God forbid a "big monster movie" take place in New ****ing York). The weak attempts at humor seem genuine, the natural response of a person pushed to the breaking point. Above and beyond that, I found them amusing. Some thought the characterization weak -- I would consider it subtle, richly-considered, and anything but the patronizing "hey, look at me, I'm the MAGICAL NEGRO" archetype-plundering of most modern literature. (A little Joseph Campbell can be a dangerous thing)
There's an "if you blink, you'll miss it" moment right at the end that answers some of the criticisms of the film (my wife's chief criticism, for instance).
I believe one "problem" with the movie is that it's intensely visceral. You have to, as I did, watch wide-eyed for the full length of the movie. If you detach yourself, as a critic, you'll completely miss all of the virtues of the film (its beautiful plotting, seamless transitions, fantastic special effects, and only mild hyperrealism) and start taking cheap potshots at it ("Damn 9/11 exploiters with their vacuous too-pretty cast and their unelegant dialogue!").
I contrast it with The Mist, which I saw a while back. I liked it because it basically brought the novella (one of my long-time favorites) to life. At the same time, I was far more aware of its quality of camerawork (and far more detached from the story) than I was with Cloverfield. So go see it, enjoy it, and try not to look at it as a member of a particular genre and so forth. Yeah, it's a "big monster movie," but a damn unique one, and I think you'll get out of it what you put in.