Remove all zeros from array

You can achieve this with one loop only. Whether this is better or more clear is a matter of personal taste I am afraid.

int[] array = {0, 5, 6, 0, 0, 2, 5};
int[] temp = new int[array.length];
int numberOfZeros = 0;
for (int i=0; i<array.length; i++){
  if (array[i] != 0){
    temp[i-numberOfZeros] = array[i];
  } else {
    numberOfZeros++;
  }
}
int[] result = new int[temp.length-numberOfZeros];
System.arraycopy(temp, 0, result, 0, result.length);

Another option would be to use a List implementation like ArrayList from which you can just remove elements, but then you will have to work with Integer instances and not with ints

List<Integer> originalList = ....;
Iterator<Integer> iterator = originalList.iterator();
while ( iterator.hasNext() ) {
  Integer next = iterator.next();
  if ( next == 0 ){
    iterator.remove();
  }
}
//convert to array if needed
Integer[] result = originalList.toArray( new Integer[originalList.size()]);

This is one of those rare cases where it is easier to show it in code than to explain in plain English:

int targetIndex = 0;
for( int sourceIndex = 0;  sourceIndex < array.length;  sourceIndex++ )
{
    if( array[sourceIndex] != 0 )
        array[targetIndex++] = array[sourceIndex];
}
int[] newArray = new int[targetIndex];
System.arraycopy( array, 0, newArray, 0, targetIndex );
return newArray;

How about this:

Integer[] numbers = {1, 3, 6, 0, 4, 0, 3};
List<Integer> list = new ArrayList<Integer>(Arrays.asList(numbers));
list.removeAll(Arrays.asList(Integer.valueOf(0)));
numbers = list.toArray(new Integer[list.size()]);
System.out.println(Arrays.toString(numbers));

OUTPUT:

[1, 3, 6, 4, 3]

With Java 8 you can make a stream out of the array, apply .filter() and then convert it back into an array :

int[] array = {0, 5, 6, 0, 0, 2, 5};

int[] filteredArray = Arrays.stream(array).filter(num -> num != 0).toArray();    

// filteredArray = {5, 6, 2, 5};