Hahahaha, no offense, Google, but yeah right. It's a wee bit too late for you to be asking users not to use the word "Google" as a verb. It's already an entry in the Merriam-Webster dictionary.
Based on the above article, however, I'm not 100% clear if they just want people to stop using it to refer to any kind of internet searching and only for actually using Google, or if they want its use to stop altogether.
Addendum: After quickly publishing this, I decided to do some blogosphere research and found this defense of Google from the Scobleizer blog. Yay, more patent and trademark stuff. :)
Also, perhaps this battle isn't new, just now more public. Check it out here and here. [Links found on Yummy Yummy]