I like to try to find some trigger that I can consider to be a record separator, and then use $/ accordingly. Here's an example wherein we use Traceroute: as the record separator. That means that the first record will be empty, since technically it shows up at the beginning of a record rather than at the end. After discarding the record separator, we can check to see if the rest of the record is empty (it will be in the case of the first time Traceroute: is seen, since nothing precedes it).

Next, in this example, we find another anchor and use it to locate the IP address that we're trying to reach. Capture that. Then count how many times a number appears at the beginning of a line (preceded by an optional space). Keep track of that count. The Lingua::EN::Inflect stuff is just for fun.

use Lingua::EN::Inflect qw( PL );

{
  local $/ = 'Traceroute';
  while( my $line = <DATA> ) {
    chomp $line;
    next unless length $line;
    my ( $destination ) = $line =~ m/\(([^)]+)\)/;
    my $count = () = $line =~ m/^\s*(\d+)\s{2}/mg;
    print "$destination: $count ", PL( "hop", $count ), ".\n";
  }
}


__DATA__
Traceroute: 11 1291796822 1291796821 1291796821 OpenDNS 0.chstatic.cvc
+dn.com 216.137.61.109
traceroute to 216.137.61.109 (216.137.61.109), 30 hops max, 60 byte pa
+ckets
 1  192.168.178.1  0.638 ms  7.361 ms  7.366 ms
 2  82.135.16.28  44.925 ms  46.633 ms  50.457 ms
 3  212.18.7.121  98.010 ms  98.307 ms  98.650 ms
 4  212.18.6.97  68.374 ms  72.222 ms  76.184 ms
 5  62.140.24.49  129.246 ms  130.224 ms  130.221 ms
 6  4.69.134.2  98.205 ms  105.207 ms  102.287 ms
 7  4.69.140.10  106.816 ms  82.609 ms 4.69.140.2  88.631 ms
 8  4.68.23.76  79.559 ms  65.093 ms 4.68.23.204  64.530 ms
 9  212.162.24.70  65.476 ms  50.797 ms  55.108 ms
10  216.137.61.109  58.221 ms  62.351 ms  59.094 ms
Query: 18 1291796822 GoogleDNS 0.chstatic.cvcdn.com 1 True 0.155671834
+946 0.0507638454437
Traceroute: 2 1291796823 1291796822 1291796822 LocalDNS LocalDNS 192.1
+68.178.1
traceroute to 192.168.178.1 (192.168.178.1), 30 hops max, 60 byte pack
+ets
 1  192.168.178.1  0.649 ms  1.033 ms  1.013 ms
Query: 13 1291796823 LocalDNS 0.media.collegehumor.com 1 True 0.193642
+139435 0.0472960472107
Traceroute: 9 1291796827 1291796822 1291796822 GoogleDNS GoogleDNS 8.8
+.8.8
traceroute to 8.8.8.8 (8.8.8.8), 30 hops max, 60 byte packets
 1  192.168.178.1  0.464 ms * *
 2  82.135.16.28  68.613 ms  72.079 ms  76.268 ms
 3  212.18.7.101  160.966 ms  163.495 ms  163.517 ms
 4  93.104.240.53  99.638 ms  103.396 ms  108.241 ms
 5  209.85.241.110  111.919 ms 209.85.240.64  114.900 ms 209.85.241.11
+0  119.654 ms
 6  209.85.254.116  124.134 ms 209.85.254.118  127.998 ms 209.85.254.1
+12  111.621 ms
 7  209.85.249.166  116.258 ms 209.85.254.126  115.774 ms 209.85.254.1
+34  105.670 ms
 8  8.8.8.8  95.428 ms  95.573 ms  95.923 ms
Query: 10 1291796827 OpenDNS 1.im.cz 1 True 0.0573320388794 0.05522108
+078
[download]

The output:

216.137.61.109: 10 hops.
192.168.178.1: 1 hop.
8.8.8.8: 8 hops.
[download]