Una solución rápida:
Código PHP:
<form method="POST" action="<?php echo $_SERVER['PHP_SELF']; ?>">
<?
$value_select = '';
if ( isset($_POST['select']) )
$value_select = $_POST['select'];
?>
<select name="select">
<option value="1" id="1" <?php if ( $value_select == 1) echo 'selected="selected"'; ?> >Valor 1</option>
<option value="2" id="2" <?php if ( $value_select == 2) echo 'selected="selected"'; ?> >Valor 2</option>
<option value="3" id="3" <?php if ( $value_select == 3) echo 'selected="selected"'; ?> >Valor 3</option>
</select>
<input type="submit" name="boton" value="Apretame" />
</form>