We have a way to notify administrators when a new user registers. This is accomplished by setting this to true in user.config
<add key="NotifyAdminsOnNewUserRegistration" value="true" />
While it does not prevent a user from signing in before approval, there is no real intrinsic permissions that result from signing in. ie they can't do anything by default that an anonymous user cannot do anyway so there is no real benefit to preventing them from signing in.
If you want to protect certain pages, you could make a role named "Members" and protect the pages with that role, then you can decide on a case by case basis whether to add the new user to that role after receiving the notification. Or the account could be locked by the administrator after he gets the notification if he does not want the user to be able to sign in.
Its also possible to disable site registration so only admins can create new site users. There could be a contact form where users could request an account.
People have asked in the past for a white list that could be used to allow only some email addresses to register. Its something we may add eventually but not a very high priority.
Hope it helps,