document.getElementById("fruit")value=jieguo;   value后面少个.      

<input type='button' value=' = ' onclick="count()"/>

value中写规范一些，双引号中最好不要有空格

 document.getElementById("fruit")value=jieguo;       差了一个点，就是document.getElementById("fruit").value=jieguo; 

document.getElementById("fruit").value=jieguo;

应写在function之外

  <script type="text/javascript">

   function count(){

var txt1   = parseInt( document.getElementById('txt1').value);//获取第一个输入框的值

var txt2   = parseInt( document.getElementById('txt2').value);//获取第二个输入框的值

var select = document.getElementById('select').value;//获取选择框的值

var result = '';

switch (select)

{

case '+':

result = txt1 + txt2;

break;

case '-':

result = txt1 - txt2;

break;

case '*':

result = txt1 * txt2;

break;

case '/':

result = txt1 / txt2;

break;  

}

         document.getElementById('fruit').value = result;//设置结果输入框的值 

   }

  </script>