Your syntax is wrong try
<select name="Category2" size="1" id="Category2" onchange="function(document.getElementById('Category1').value);">
pass value of category1 as argument when change happens to select
.
OP Comment Response
<script type="text/javascript">
function changeFunction(cat)
{
alert(cat);
}
</script>
<select name="Category1" size="1" id="Category1" >
<option value="Item1">Item1</option>
<option value="Item2">Item2</option>
<option value="Item3">Item3</option>
<option value="Item4">Item4</option>
<option value="Item5">Item5</option>
<option value="Item6">Item6</option>
</select>
<select name="Category2" size="1" id="Category2" onchange="changeFunction(document.getElementById('Category1').value);">
<option value="A">A</option>
<option value="B">B</option>
<option value="C">C</option>
<option value="D">D</option>
<option value="E">E</option>
<option value="F">F</option>
<option value="G">G</option>
<option value="H">H</option>
</select>
above code is tested now check i am sure it will work.