None of these answers ended up working for my Git credential issue. Here is what did work if anyone needs it (I’m using Git 1.9 on Windows 8.1).
To update your credentials, go to Control Panel → Credential Manager → Generic Credentials. Find the credentials related to your Git account and edit them to use the updated password.
Reference: How to update your Git credentials on Windows
Note that to use the Windows Credential Manager for Git you need to configure the credential helper like so:
git config --global credential.helper wincred
If you have multiple GitHub accounts that you use for different repositories, then you should configure credentials to use the full repository path (rather than just the domain, which is the default):
git config --global credential.useHttpPath true