user14761: I am using an Arduino Mega and a 12864ZW LCD with the u8glib library and the following code to draw to the LCD:
U8GLIB_ST7920_128X64 Display(LCD_E_PIN, LCD_RW_PIN, LCD_RS_PIN, U8G_PIN_NONE);

void loop(){
   Draw();
}

void Draw(){
   Display.firstPage();

   do{
      Display.setPrintPos(10, 10);
      Display.print("This is a test");
   }while(Display.nextPage());
}

The problem is that the display is constantly redrawing itself. When I used LCD displays in the past, they usually only required to write to the LCD once unless you wipe the display. When I adjusted the code to:
U8GLIB_ST7920_128X64 Display(LCD_E_PIN, LCD_RW_PIN, LCD_RS_PIN, U8G_PIN_NONE);
bool needsUpdate = true;

void loop(){
   Draw();
}

void Draw(){
   if (needsUpdate){
       Display.firstPage();
       do{
          Display.setPrintPos(10, 10);
          Display.print("This is a test");
       }while(Display.nextPage());
       needsUpdate = false;
   }
}

I do not get anything drawn on the LCD. Is there a parameter that needs to be set so I only have to redraw the LCD if something changes? Am I using an outdated library? Is there a better library I should be using?
EDIT
I think the main problem I have with using this library is does the Draw loop need to be executed continuously to display on the LCD or is there a way to only draw the screen once until it is needed to be drawn again?

user3917: You haven't shown us all the code – in particular, the call to Draw() from loop() is missing – so this answer is speculative, based on the assumption your loop() is as follows. 
void loop(void) {
    Draw();
}

If so, your first bit of code will constantly redraw because loop() runs repeatedly without delay.  Try adding a delay(1000); after Draw() in that case.
Your second bit of code will begin by drawing your image once, and in that Draw() call it will set needsUpdate to false.  Then loop() runs again, and the firstPage() call erases the screen.  Since needsUpdate now is false and remains false, subsequent calls don't draw an image.
Rather than putting your picture loop into Draw(), perhaps use Draw() just to draw primitives, and keep your controls in loop(): 
void loop(void) {
  Display.firstPage();  
  do {     // picture loop
    Draw();
  } while( Display.nextPage() );    
  delay(1000); // delay before next picture
}

If you still get repeated fast redraws, for troubleshooting comment out the do and } while lines.

user14761: Much thanks to jwpat7 for getting me on the right track with this. So I found out how this LCD should really be setup. I am not sure why the examples I was able to find online and even on the u8glib wiki showed the usage like my question but I was able to get this library functioning right. 
First thing is the .firstPage() and .nextPage() functions. The .firstPage() function actually clears the screen and the .nextPage() function displays what is waiting in the queue (thanks jwpat7). When the .nextPage() finishes there is no need to write to the LCD again until you need a refresh. I put together a very simple code example that uses a input to change the text without having to continuously update the LCD.
U8GLIB_ST7920_128X64 Display(LCD_E_PIN, LCD_RW_PIN, LCD_RS_PIN, U8G_PIN_NONE);
bool redraw = true;
String strOut = "This is a test...";

void loop() {

    if (redraw){
        Display.firstPage();  //Clear the LCD

        //Main Difference while the LCD needs drawing will return 1
        while(Display.nextPage()){
            Display.setFont(u8g_font_04b_03b);
            Display.setPrintPos(20, 20);
            Display.print(strOut);
        }

        redraw = false;  //Clear flag to redraw
    }

    //check if any of the pins in PINA have been pressed 
    if (~PINA & 0xff){
        strOut = "Of the emergency broadcast ...";

        redraw = true; //Set flag to redraw the screen
    }
}


14761: <p>I am using an Arduino Mega and a 12864ZW LCD with the u8glib library and the following code to draw to the LCD:</p>

<pre><code>U8GLIB_ST7920_128X64 Display(LCD_E_PIN, LCD_RW_PIN, LCD_RS_PIN, U8G_PIN_NONE);

void loop(){
   Draw();
}

void Draw(){
   Display.firstPage();

   do{
      Display.setPrintPos(10, 10);
      Display.print("This is a test");
   }while(Display.nextPage());
}
</code></pre>

<p>The problem is that the display is constantly redrawing itself. When I used LCD displays in the past, they usually only required to write to the LCD once unless you wipe the display. When I adjusted the code to:</p>

<pre><code>U8GLIB_ST7920_128X64 Display(LCD_E_PIN, LCD_RW_PIN, LCD_RS_PIN, U8G_PIN_NONE);
bool needsUpdate = true;

void loop(){
   Draw();
}

void Draw(){
   if (needsUpdate){
       Display.firstPage();
       do{
          Display.setPrintPos(10, 10);
          Display.print("This is a test");
       }while(Display.nextPage());
       needsUpdate = false;
   }
}
</code></pre>

<p>I do not get anything drawn on the LCD. Is there a parameter that needs to be set so I only have to redraw the LCD if something changes? Am I using an outdated library? Is there a better library I should be using?</p>

<p><strong>EDIT</strong></p>

<p>I think the main problem I have with using this library is does the Draw loop need to be executed continuously to display on the LCD or is there a way to only draw the screen once until it is needed to be drawn again?</p>
 3917: <p><strike>You haven't shown us all the code – in particular, the call to <code>Draw()</code> from <code>loop()</code> is missing – so this answer is speculative, based on the assumption</strike> your <code>loop()</code> is as follows. </p>

<pre><code>void loop(void) {
    Draw();
}
</code></pre>

<p><strike>If so,</strike> your first bit of code will constantly redraw because <code>loop()</code> runs repeatedly without delay.  Try adding a <code>delay(1000);</code> after <code>Draw()</code> in that case.</p>

<p>Your second bit of code will begin by drawing your image once, and in that <code>Draw()</code> call it will set <code>needsUpdate</code> to false.  Then <code>loop()</code> runs again, and the <code>firstPage()</code> call erases the screen.  Since <code>needsUpdate</code> now is false and remains false, subsequent calls don't draw an image.</p>

<p>Rather than putting your picture loop into <code>Draw()</code>, perhaps use <code>Draw()</code> just to draw primitives, and keep your controls in <code>loop()</code>: </p>

<pre><code>void loop(void) {
  Display.firstPage();  
  do {     // picture loop
    Draw();
  } while( Display.nextPage() );    
  delay(1000); // delay before next picture
}
</code></pre>

<p>If you still get repeated fast redraws, for troubleshooting comment out the <code>do</code> and <code>} while</code> lines.</p>
 14761: <p>Much thanks to jwpat7 for getting me on the right track with this. So I found out how this LCD should really be setup. I am not sure why the examples I was able to find online and even on the u8glib wiki showed the usage like my question but I was able to get this library functioning right. </p>

<p>First thing is the .firstPage() and .nextPage() functions. The .firstPage() function actually clears the screen and the .nextPage() function displays what is waiting in the queue (thanks jwpat7). When the .nextPage() finishes there is no need to write to the LCD again until you need a refresh. I put together a very simple code example that uses a input to change the text without having to continuously update the LCD.</p>

<pre><code>U8GLIB_ST7920_128X64 Display(LCD_E_PIN, LCD_RW_PIN, LCD_RS_PIN, U8G_PIN_NONE);
bool redraw = true;
String strOut = "This is a test...";

void loop() {

    if (redraw){
        Display.firstPage();  //Clear the LCD

        //Main Difference while the LCD needs drawing will return 1
        while(Display.nextPage()){
            Display.setFont(u8g_font_04b_03b);
            Display.setPrintPos(20, 20);
            Display.print(strOut);
        }

        redraw = false;  //Clear flag to redraw
    }

    //check if any of the pins in PINA have been pressed 
    if (~PINA &amp; 0xff){
        strOut = "Of the emergency broadcast ...";

        redraw = true; //Set flag to redraw the screen
    }
}
</code></pre>
