When a user doesn't show up on the logon screen

A user wondered why a Windows account vanished from the list of users in the logon screen and Control Panel. After doing some quick experiments, I found that at least these two conditions need to be satisfied for the user to appear:

• The user account must be enabled. If it's disabled, use net user username /active:yes
• The user is a member of at least one of the Users or Administrators groups. If it's not, add it to one of those with net localgroup Users username /add