I think your script is great, so forgive me if this seems
a bit nit-picky :)

I think you could improve your script like so ...
change

  my $sock;
  my @openports = ();
  my $i = -1;

  print "Scanning $host for open ports.....\n\n";
  foreach my $cport (@ports) {
      $sock = IO::Socket::INET->new(PeerAddr => $host,
                                  PeerPort => $cport,
                                  Proto => $proto);
      if($sock) {
          $i++;
          $openports[$i] = $cport;
      }
  }
[download]

... to ...

  my $sock;
  my @openports = ();


  print "Scanning $host for open ports.....\n\n";
  foreach my $cport (@ports) {
      $sock = IO::Socket::INET->new(PeerAddr => $host,
                                  PeerPort => $cport,
                                  Proto => $proto);
      if($sock) {
          push ( @openports, $cport);
      }
  }
[download]

... that $i = -1 thing bugs me :/
But good example of a port scanner!