I just wanted to mention that ALL Dropbox users will be auto updated to the current stable client within the next few weeks. As notes By Arash F. of Dropbox.
You all may see prompts for an update asking for your password this is normal for the change to occur, If you would like more info you can find it in the thread I link to below and or the main Dropbox forums.
It is asking for you admin password for the computer you are running it is NOT asking for the Dropbox Password, or any others. The reason the password is needed is for the installer to make the needed changes to the application etc.