Hey, I suggest DockDodger.
Simply download and unzip it. Open it, and it will tell you to drag whatever app you don't want to show up on your dock, into the DockDodger window. Enter your password. Quit the app you chose (if it's open), and open it again.
The Dock icon should be gone.
🙂
You can download it here, at macupdate:
http://www.macupdate.com/info.php/id/24427/dock-dodger
*The latest comment on macupdate says this app does not work anymore. This is false. I have just tested this with Firefox, and it works great.*