do you know if its possible that users can also have with their accounts an email?

do you know if there is a plugin for that?

for example if they register that they have also with their account an email and receive those messages in their in box or something like that

lets say my website is www.example.com

and lets say my user want to register with the name userexample.

now his account is userexample and have also an email with userexample@example.com

do anyone know if there is a plugin for that?