User getting login prompt for the site even when logged into domain

This is a common issue that seems weird because it happens to just a few people in your domain.
So a few will keep getting annoyed with the login-prompt every time they access the SharePoint site even when they are already logged-into the domain.

Perform following steps on every individual's machine who is facing the problem:
Open IE --> Internet Options --> Security --> Custom level --> Select ‘Automatic logon with current user name and password’ for User Authentication/Logon.