How can you get an Android user’s email address?

Why you wanna do that?

import android.accounts.Account;
import android.accounts.AccountManager;
import android.content.Context;

/**
 * This class uses the AccountManager to get the primary email address of the
 * current user.
 */
public class UserEmailFetcher {

  static String getEmail(Context context) {
    AccountManager accountManager = AccountManager.get(context); 
    Account account = getAccount(accountManager);

    if (account == null) {
      return null;
    } else {
      return account.name;
    }
  }

  private static Account getAccount(AccountManager accountManager) {
    Account[] accounts = accountManager.getAccountsByType("com.google");
    Account account;
    if (accounts.length > 0) {
      account = accounts[0];      
    } else {
      account = null;
    }
    return account;
  }
}

In your AnroidManifest.xml

<uses-permission android:name="android.permission.GET_ACCOUNTS" />