For some of the sites, such as security, parenting and the workplace, it would be useful to be able to ask questions anonymously. For example, someone might want to ask about issues that could either lead to a security compromise, be embarrassing for their children later on or possibly lose them their job.
On those sites it is possibly to log out (not on Stack Overflow), but this doesn't provide you with notifications when the questions are answered.
Should there be an option to post anonymously? Asks for the same feature, but for answers
Should there be anonymous answers (and questions)? Asks about this for a different reason