The Visual Effects for Cloverfield have been done by a company in London called Double Negative. Their Currently in Production list shows Cloverfield, Dark Knight, Harry Potter, among others. Some of their past work includes Stardust, Bourne Ultimatum, DaVinci Code, and Casino Royal. You can see a video of their past work on their Showreel page.
* Thanks to Foomandoonian from the podcast for finding this.
** Speaking of the podcast, I wasn't able to finish editing it last night, so look for it sometime tomorrow!