When sending out email blasts that you want someone to be able to reply to, most people set the from address on the campaign to a valid email address. Unfortunately, this means that any auto-replies will show up in your mailbox. You can combat this often within your email client by setting up filters for emails with key phrases such as "out of office" to remove a lot of the problem, but this is not a 100% fix.
Alternately, if you are sending emails that do not require users have the ability to reply (sales notifications, etc) then you can set your from email to a standard business email that is not connected to any individual person (i.e. email@example.com) to avoid getting the out of office replies littering one specific email address. If you follow this method, it is good practice to make sure that you have either created the email address or created a catch-all account so that any replies will still go through and can be sifted through at some point after the campaign.
An older method was to use no-reply email addresses for your email marketing campaigns. However, this article outlines several reasons why no-reply email addresses are often considered a bad marketing practice in today's marketing world as well as a few other options for dealing with out of office replies.