The mystery isn't just what kind of "thing" is freaking out all those anonymous New York City partygoers.
I'd like to know, and you might, too - what's with the title?
Nothing's a sure bet, but here at the Fandango offices, just right down the street from Abrams' Bad Robot production company, we've come up with a couple of theories.
Cloverfield is the street right around the corner from Bad Robot's old offices on Olympic Boulevard. As reported previously on Slash Film, it's also the original name (Clover Field) of the Santa Monica airport -- where the first successful around-the-world-flight was launched in 1924.
*The view from Olympic Boulevard, a few blocks from J.J. Abrams' former production office:

Another interesting factoid: During World War II, aircraft pioneer Donald Douglas, along with set designers from Warner Bros. studios, canopied the hangars, buildings and parking lots under an umbrella of 5 million square feet of chicken wire.
On top of that mesh, they created light-weight houses, clotheslines and fake trees to camoflauge the base (used to manufacture military aircraft) from any possible air attacks. They also spray painted the landing strip to look like a field of grass.
Maybe Cloverfield's monster uses New York City and its jungle of skyscrapers and urban sprawl as its own sort of hide and seek canopy? Perhaps it's a term used in the film by official-types to describe the monster's origin and/or movements?
Who knows? It could be that the title's never explained. But, it's a great way (along with the mysterious trailers and teasers - check out this online exclusive spot) to pique maximum curiosity.
Two more bits of interest:
Clover Field founder Douglas created the Aero Theater (for aerospace) in Santa Monica to keep up the morale of his workers during the war. It operated around the clock showing all of Hollywood's latest product. Today, it's one of two venues featuring special movie presentations from the esteemed American Cinematheque (the other venue being the Egyptian Theater in Hollywood).
Also, if you're on the west side of L.A., check out Clover Park, right near the SM Airport - it's a nice expanse of grassy fields and playgrounds in the middle of our own urban sprawl...as far as we know, they don't allow monsters there.
UPDATE! The real, real reason it's called Cloverfield? Here's a quote from the movie's director Matt Reeves from a recent interview with website LAist ...
"When we started the project there was going to be an announcement in the trades. In this case, they wanted to keep everything under wraps. So the movie was going to be made under this outside corporation that was basically a property of Paramount. That corporation had a name that I don’t know the name of. I think Clover was the first part of it. Maybe it was Cloverdale. When Drew [Goddard, LOST writer] was putting a name to the project, there was supposed to be a name for the project like there was for The Manhattan Project. So he said, "I am going to use that weird mysterious thing," and he misheard it. He didn’t even understand that it wasn’t Cloverfield, it was Cloverdale. Maybe that was because of the street by J.J.’s old office, but the truth is he just misunderstood it."
So much for our theories...although we still kinda like em. :)