Let users enter their password when registering?

I would like to let new users to input their desired password in the same registration form when they are registering on my WP site.

As you know by default the registration form only asks the new user to enter username and email, after that the system will email the user with a generated password. But I dont want it, this is not suitable for my website since it doesnt have mail function working(it's a free hosting service).

Thank you ver开发者_JS百科y much for all your kind help. Any help is greatly appreciated!

*It's ok if I must edit the core files of wordpress, thank you! Please kindly guide me.

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This plugin will allow your users to create their own passwords when registering for your site http://wordpress.org/extend/plugins/theme-my-login/