Of course! You do not need to link JibJab to Facebook, or even have a Facebook account in order to use JibJab.
To log into an existing account click the "Menu" button in the right hand corner (it should look like three lines stacked on top of each other), and select "Log In" from the menu. Then enter the email and password you used to create the account. They do NOT need to be associated with a Facebook account.
To create a new account, click the "Sign Up" button and then enter the email address and password you would like to use with JibJab. The email and password you use to NOT need to be associated with Facebook in any way.
If you are linked to Facebook unintentionally, please follow these directions to unlink your Facebook account.