Screen Sharing with Mac (username + password) authentication

Go to System Preferences > Screen Sharing and make sure you've either:

1. Set Allow Access For to All Users
   
   or

2. Set Allow Access For to Only These Users, and add your user to the list

Screen Sharing with VNC (password-only) authentication

Go to System Preferences > Sharing > Screen Sharing (or Apple Remote Desktop), click the Computer Options button, and enter a new password.

Vine Server

If you're using Vine Server, go to its Preferences, then enter a new password, and enter the same new password in iTeleport as well.

If you get the Too Many Security Failures error, just click the Restart Server button in Vine Server to reset it.