All of the following sites allow you to register your email address with them. In addition to your name and email address, most also ask for a few other items of personal information.

To get you started, here's the registration box for Reunion.com, one of the largest email search engines...

Create your FREE Reunion.com account
 
First Name Current Last Name
 
Maiden Name (Leave blank if n/a) Email
 
Birthday (mon/dd/yyyy) Gender
  Male    Female
Zip/Postal Code  
 

To continue registering your email address elsewhere, select any of the directories listed below - each link will take you straight to the registration page.

Note that not all directories update their public information instantly - some only refresh the data every few weeks. However, before long you should be "visible" on the web for your friends and family to find you if they come looking.