If it is inconvenient to ask the mail man in plain text, make sure that the man himself has written. Ask the person whose e-mail address you need to know to mail you a card or something, interesting song that you can't find online or something like that.
You can make a few personal questions and use a phone to conduct a survey. At the end of the conversation ask the person to provide contact data – in this case it will be the email address.
If you know the name and surname of the person whose mailbox you need to learn, try to find it in one of the social networks. For example, in "My world" or "Vkontakte" information about the user can be in the public domain. Try your luck – you might just find the desired person and know his / her e-mail. In some social networks, e-mail address is mandatory to specify.
If you know the place of work or study of the person, contact the Dean's office or office Manager and ask them to tell mail the employee/student to convey to him something important. Your common friends and acquaintances will certainly be able to help you to seize necessary information.
Use paid services on the Internet that are engaged in the search of the person, but rather information about it (for example, To ensure absolute accuracy you no one will, but as an extreme measure, this option is ideal.