I'm unclear why you cannot use UNIQUE DISTINCT in your SQL query, but you can use a hash to check if you've seen a given data value already. You've not made it clear what you expect to be unique, but if you assume that "user" should only be displayed once, you might want something like:

$user_data = "
<table cellpadding=\"0\" cellspacing=\"0\">
<thead>
 <tr>
  <td colspan=\"4\">User List</td>
 </tr>
</thead>";

my %seen;
for (my $i = 0; $i < @$sql_data; $i++) {
    my $user = $sql_data->[$i]{user};
    
    if ($seen{$user}) { # <-- added flow control
        next;
    }
    $seen{$user} = 1;
    
    my $link = "<a href=\"goto.pl?user=$user\">$user</a>";
    my $first = $sql_data->[$i]{first};
    my $last = $sql_data->[$i]{last};
    my $phone = $sql_data->[$i]{phone};
    my $mail = $sql_data->[$i]{mail};
                                
    $user_data = "$user_data<tr><td><div>$show</div></td><td><div>$las
+t, $first</div></td><td>$phone</td><td><div>$email</div></td></tr>";
}
$user_data = "$user_data</table>";
[download]

If your condition is more complex, you can use a list of lists (perllol) to check uniqueness in a parallel fashion.

Update: Changed UNIQUE to DISTINCT above. Not quite sure why I always forget that keyword. Thanks, roboticus.