Binary counter with 16 Leds

I have read you right Mike Void (display) instead of Void (loop)?

No you always need a loop, you need the display as well, and you call it anywhere you want. Here I have put it in the setup();

//**************************************************************//
//  Name    : shiftOutCode, Hello World                                
//  Author  : Carlyn Maw,Tom Igoe, David A. Mellis 
//  Date    : 25 Oct, 2006    
//  Modified: 23 Mar 2010                                 
//  Version : 2.0                                             
//  Notes   : Code for using a 74HC595 Shift Register           //
//          : Display specified value                          
//****************************************************************

//Pin connected to ST_CP of 74HC595
int latchPin = 8;
//Pin connected to SH_CP of 74HC595
int clockPin = 12;
////Pin connected to DS of 74HC595
int dataPin = 11;


void setup() {
  //set pins to output so you can control the shift register
  pinMode(latchPin, OUTPUT);
  pinMode(clockPin, OUTPUT);
  pinMode(dataPin, OUTPUT);
    Serial.begin(9600);
  Serial.println("reset");
       display(43690);
}

void loop(){
}

void display(unsigned int numberToDisplay){
    digitalWrite(latchPin, LOW);
    shiftOut(dataPin, clockPin, MSBFIRST, numberToDisplay % 256);  //lower byte
    shiftOut(dataPin, clockPin, MSBFIRST, numberToDisplay / 256); // higher byte
    digitalWrite(latchPin, HIGH);
}