@kavi: This will not work as the email is not part of the user class but of the datatype account. And changing a datatype is not easily done...
@satheesh: The main code for the ezuser datatype can be found in \kernel\classes\datatypes\ezuser\ezusertype.php but modifying it seems risky to me. To many features (notification, forgotpassword and whatever else) make use of this datatype so you could seriously compromise your system.
If you really don't want it, you can get rid of it by prefilling it with some random email <timestamp>@blackhole.nada (it has to be unique and you can modify the edit template to put that into a hidden field as it has to be unique.
the edit template is into design/standard/template/content/datatype/edit/ezuser.tpl
As Claudia said, that's quite often used by various features, not having emails might comes as a problem later...