Integer division without using / or *

divide.js

var divide = function (dividend, divisor) {
  // Handle 0 divisor
  if (divisor === 0) {
    return NaN;
  }
  
  // Handle negative numbers
  var isNegative = false;
  if (dividend < 0) {
    // Change sign
    dividend = ~dividend+1;
    isNegative = !isNegative;
  }
  
  if (divisor < 0) {
    // Change sign
    divisor = ~divisor+1;
    isNegative = !isNegative;
  }
  
  /**
   * Main algorithm
   */
  
  var result = 1;
  var denominator = divisor;
  // Double denominator value with bitwise shift until bigger than dividend
  while (dividend > denominator) {
    denominator <<= 1;
    result <<= 1;
  }
  
  // Subtract divisor value until denominator is smaller than dividend
  while (denominator > dividend) {
    denominator -= divisor;
    result -= 1;
  }
  
  // If one of dividend or divisor was negative, change sign of result
  if (isNegative) {
    result = ~result+1;
  }
  
  return result;
}

console.log(divide(-16, 3)); // -5
console.log(divide(16, 3)); // 5
console.log(divide(16, 33)); // 0
console.log(divide(16, 0)); // NaN
console.log(divide(384, 15)); // 25

This solution does not handle decimal results, it only handles the largest integer division, but could easily return the remainder (dividend - denominator).