Use a while loop above input line as:

 while(true)

And, use if condition to break.

if(year == 0)
    break;

Also, condition for leap year is wrong in your code. It should be:

if((year % 100 == 0 && year % 400 == 0) || (year % 4 == 0 && year % 100 != 0))
    //its a leap year
else
    //its not

PS: As in comments, I'll give a complete code:

import java.util.*;

public class Task10 {

public static void main(String[] args) {
    System.out.println("Enter a year to check if it is a leap year");
    while(true){
    Scanner input = new Scanner(System.in);
        int year = input.nextInt();
        if(year == 0)
            break;
        if((year % 100 == 0 && year % 400 == 0) || (year % 4 == 0 && year % 100 != 0))
            System.out.println(year + " is a leap year");
        else
            System.out.println(year + " is not a leap year");
    }
}

}

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Easy with do-while:

Scanner keyboard = new Scanner(System.in);
int startr, endr;
boolean good = false;
do
{
  System.out.println("Enter the Starting Number of the Range: ");
  startr = keyboard.nextInt();
  if(startr % 10 == 0 && startr >= 0)
    good = true;
  else
    System.out.println("Numbers is not divisible by 10");
}
while (!good);

good = false;
do
{
    System.out.println("Enter the Ending Number of the Range: ");
    endr = keyboard.nextInt();
    if(endr % 10 == 0 && endr <= 1000)
      good = true;
    else
      System.out.println("Numbers is not divisible by 10");
}
while (!good);

// do stuff

You have to assign repeat in your while-loop so it becomes false if the user says yes:

repeat = !input.equalsIgnoreCase("yes");