您正在调用mysql_fetch_array两次...一次在循环之前，另一次在循环过程中。
如果您需要一个种子行来构建标题行，那么最好在这里使用do.. while循环。

$query = "SELECT * FROM members";
$results = mysql_query($query);
$row = mysql_fetch_assoc($results);

//echo my <table> start and headings;

do  
{
    echo "<tr><td>".$row['Last Name']."</td>";
    echo "<td>".$row['First Name']."</td>";
    echo "<td>".$row['Middle Name']."</td>";
    echo "<td>".$row['Sfx']."</td>";
    echo "<td>".$row['Prf']."</td>";
    echo "<td>".$row['Spouse/SO']."</td>";
    echo "<td>".$row['Ancestor']."</td>";
    echo "<td>".$row['Status']."</td>";
    echo "<td>".$row['Address 1']."</td>";
    echo "<td>".$row['Address 2']."</td>";
    echo "<td>".$row['City']."</td>";
    echo "<td>".$row['ST']."</td>";
    echo "<td>".$row['Zip 5']."</td>";
    echo "<td>".$row['Zip 4']."</td>";
    echo "<td>".$row['Home Phone']."</td>";
    echo '<td><a href="mywebsite/mypage.php?id=' . $row['id'] . '">Bio</a></td></tr>';
} while ($row = mysql_fetch_assoc($results));

echo "</table><hr>";

$query = "SELECT * FROM members";
$results = mysql_query($query);
$row = mysql_fetch_array($results); <-- There's your first row. Remove this.

程式码中有额外的mysql_fetch_array。此外，也遗漏开头数据表标记（<table>）。
更正代码：

$query = "SELECT * FROM members";
$results = mysql_query($query);
echo "<table>";

while ($row = mysql_fetch_array($results)) 
{
echo "<tr><td>".$row['Last Name']."</td>";
echo "<td>".$row['First Name']."</td>";
echo "<td>".$row['Middle Name']."</td>";
echo "<td>".$row['Sfx']."</td>";
echo "<td>".$row['Prf']."</td>";
echo "<td>".$row['Spouse/SO']."</td>";
echo "<td>".$row['Ancestor']."</td>";
echo "<td>".$row['Status']."</td>";
echo "<td>".$row['Address 1']."</td>";
echo "<td>".$row['Address 2']."</td>";
echo "<td>".$row['City']."</td>";
echo "<td>".$row['ST']."</td>";
echo "<td>".$row['Zip 5']."</td>";
echo "<td>".$row['Zip 4']."</td>";
echo "<td>".$row['Home Phone']."</td>";
echo '<td><a href="mywebsite/mypage.php?id=' . $row['id'] . '">Bio</a></td></tr>';
}

echo "</table><hr>";

初始化$row时调用mysql_fetch_array，读取第一行，然后在开始while循环时第二次调用它，在循环运行之前将它移动到第二行，因此它不会对第一行执行任何操作。

while ($row) 
{
echo "<tr><td>".$row['Last Name']."</td>";
echo "<td>".$row['First Name']."</td>";
echo "<td>".$row['Middle Name']."</td>";
echo "<td>".$row['Sfx']."</td>";
echo "<td>".$row['Prf']."</td>";
echo "<td>".$row['Spouse/SO']."</td>";
echo "<td>".$row['Ancestor']."</td>";
echo "<td>".$row['Status']."</td>";
echo "<td>".$row['Address 1']."</td>";
echo "<td>".$row['Address 2']."</td>";
echo "<td>".$row['City']."</td>";
echo "<td>".$row['ST']."</td>";
echo "<td>".$row['Zip 5']."</td>";
echo "<td>".$row['Zip 4']."</td>";
echo "<td>".$row['Home Phone']."</td>";
echo '<td><a href="mywebsite/mypage.php?id=' . $row['id'] . '">Bio</a></td></tr>';
  $row = mysql_fetch_array($results);

}

echo "</table><hr>";

要解决此问题，只需注解掉该行$row = mysql_fetch_array($results);。查询将提取该行之后的每一行。