The official Cloverfield facebook page is at facebook.com/cloverfieldmovie.
I mentioned this in passing in another post, but I just noticed there is another contest on the facebook page! All you have to do is log into your facebook account and "become a fan" of the Cloverfield Fan Profile.
The prize is a Panasonic HDC-SD1 AVCHD 3CCD High Definition SD/SDHC Camcorder (approximate retail value ("ARV") of $1,000.00)! The winner will be randomly selected from all eligible entries.
See the official rules for details.
* Don't forget about the Widget contest! If you are going to create a Facebook page for this contest anyway, why not add the Cloverfield widget to it? :)