Note that these steps will completely remove the SpiderOak installation from a given device. If you choose to install SpiderOak later on this device, SpiderOak will treat it as a completely new installation.
Mac: Your Mac remembers the credentials from your old account because the SpiderOak app data which stores your profile/user information is not stored in the same location as the SpiderOak app itself. This means that when you drag and drop SpiderOak in the trash, you're not actually uninstalling the app: you're just deleting the executable file. This is actually true for a lot of applications on Mac: it's part of how this operating system works.
To uninstall on a Mac, please open Finder and look in YOUR_USER_DIRECTORY. From there, open the Library folder, then Application Support. (To access the Library folder on Lion: 1.) Open up a Finder window 2.) From the "Go" menu, select "Go to Folder…" 3.) Enter "/Users//Library" and click "Go") Please delete or rename the SpiderOak folder.
Windows: To uninstall SpiderOak on Windows, first close SpiderOak (otherwise you will still have scripts running which will write more information to your appdata folder). Next, choose 'Run' from your Start menu on your PC, then type %appdata% in the Open prompt box. This will open an Explorer window called "Application Data" which lists folders for all the applications you have installed on your computer. There will be a folder in here named "SpiderOak": delete the SpiderOak folder.
Linux: Delete your ~/.SpiderOak folder Once this folder is deleted, restart SpiderOak. You'll be prompted for your username and password and you can sign in to your new account.