In the early days of the Internet, one of the key features was anonymity. No one online knew who you were if you didn't want them to.
Naturally, this caused some problems with trolls and other lowlifes ruining online discussions, sending hateful emails to people and generally being unlikable. If you think no one knows who you are, why play by the rules, right?
So, a lot of people called for less anonymity online, and that's what happened. These days, anonymity is a little harder to come by.
Advertisers track you. The government tracks you. You have a Facebook and other social media accounts tied to an email address. Your email address is tied to a profile your provider maintains. Information about you is everywhere.
A quick Google search or trip to a people search site turns up your entire life. So, the anonymity is gone, but somehow the unlikable people are still with us and causing problems. Figures.
Still, being anonymous isn't impossible. In fact, if you want to send an anonymous email or message, it's entirely possible.
Caution: While you can fool most people with these tricks, don't harass people or do anything illegal. Law enforcement can still find ways to track you down, as General Petraeus and Paula Broadwell found out a few years back. So, don't think you're completely invisible.