Dropbox doesnt have a uninstaller so in short ~
Click the "Dropbox" menu at the top of the screen next to the clock and select the "Quit" option. You can skip this step if Dropbox isn't running.
Click the "Finder" icon in the Dock to open open a new window. Click the "Applications" shortcut on the left side of the window to enter the Applications folder.
Locate "Dropbox" in the Applications folder. Then drag "Dropbox" to the Trash icon in the Dock to delete it.
Click "Macintosh HD" in the left side of the Finder window. If you've renamed your system hard drive, click its icon instead.
Open the "Library" folder, then the "Contextual Menu Items" folder. Drag the "DropboxHelperTools" folder to the Trash icon in the Dock.
Click your user name in the left side of the Finder window to go to your home folder. Drag the "Dropbox" folder to the Trash icon in the Dock. If you want to keep the files in your Dropbox folder, skip this step.
Open Trash and click empty.
To even make it easier if you download
http://download.cnet.com/AppTrap/3000-2096_4-10867505.html this will install in your System Preferences. Once its enabled, quit DB in the MenuBar, goto Applications and drag the DB icon to the trash and Apptrap will trash all associated files for you and ask if you want to trash them and then empty trash.
Done and done