You can use a hash where the keys are the IPs and the values are the count:

use strict;
use warnings;
use Regexp::Common qw/net/;

my %hash;

while (<DATA>) {
    $hash{$1}++ if /($RE{net}{IPv4})/;
}

print "$_ => $hash{$_}\n" for keys %hash;

my $uniqueIPs = keys %hash;

print "Number of unique IPs: $uniqueIPs";

__DATA__
127.0.0.1 - - [10/Apr/2007:10:39:11 +0300] "GET / HTTP/1.1" 500 606 "-
+" "Mozilla/5.0 (X11; U; Linux i686; en-US; rv:1.8.1.3) Gecko/20061201
+ Firefox/2.0.0.3 (Ubuntu-feisty)"
127.0.0.1 - - [10/Apr/2007:10:39:11 +0300] "GET /favicon.ico HTTP/1.1"
+ 200 766 "-" "Mozilla/5.0 (X11; U; Linux i686; en-US; rv:1.8.1.3) Gec
+ko/20061201 Firefox/2.0.0.3 (Ubuntu-feisty)"
139.12.0.2 - - [10/Apr/2007:10:40:54 +0300] "GET / HTTP/1.1" 500 612 "
+-" "Mozilla/5.0 (X11; U; Linux i686; en-US; rv:1.8.1.3) Gecko/2006120
+1 Firefox/2.0.0.3 (Ubuntu-feisty)"
139.12.0.2 - - [10/Apr/2007:10:40:54 +0300] "GET /favicon.ico HTTP/1.1
+" 200 766 "-" "Mozilla/5.0 (X11; U; Linux i686; en-US; rv:1.8.1.3) Ge
+cko/20061201 Firefox/2.0.0.3 (Ubuntu-feisty)"
127.0.0.1 - - [10/Apr/2007:10:53:10 +0300] "GET / HTTP/1.1" 500 612 "-
+" "Mozilla/5.0 (X11; U; Linux i686; en-US; rv:1.8.1.3) Gecko/20061201
+ Firefox/2.0.0.3 (Ubuntu-feisty)"
127.0.0.1 - - [10/Apr/2007:10:54:08 +0300] "GET / HTTP/1.0" 200 3700 "
+-" "Mozilla/5.0 (X11; U; Linux i686; en-US; rv:1.8.1.3) Gecko/2006120
+1 Firefox/2.0.0.3 (Ubuntu-feisty)"
127.0.0.1 - - [10/Apr/2007:10:54:08 +0300] "GET /style.css HTTP/1.1" 2
+00 614 "http://pti.local/" "Mozilla/5.0 (X11; U; Linux i686; en-US; r
+v:1.8.1.3) Gecko/20061201 Firefox/2.0.0.3 (Ubuntu-feisty)"
127.0.0.1 - - [10/Apr/2007:10:54:08 +0300] "GET /img/pti-round.jpg HTT
+P/1.1" 200 17524 "http://pti.local/" "Mozilla/5.0 (X11; U; Linux i686
+; en-US; rv:1.8.1.3) Gecko/20061201 Firefox/2.0.0.3 (Ubuntu-feisty)"
127.0.0.1 - - [10/Apr/2007:10:54:21 +0300] "GET /unix_sysadmin.html HT
+TP/1.1" 200 3880 "http://pti.local/" "Mozilla/5.0 (X11; U; Linux i686
+; en-US; rv:1.8.1.3) Gecko/20061201 Firefox/2.0.0.3 (Ubuntu-feisty)"
217.0.22.3 - - [10/Apr/2007:10:54:51 +0300] "GET / HTTP/1.1" 200 34 "-
+" "Mozilla/5.0 (X11; U; Linux i686; en-US; rv:1.8.1.3) Gecko/20061201
+ Firefox/2.0.0.3 (Ubuntu-feisty)"
217.0.22.3 - - [10/Apr/2007:10:54:51 +0300] "GET /favicon.ico HTTP/1.1
+" 200 11514 "-" "Mozilla/5.0 (X11; U; Linux i686; en-US; rv:1.8.1.3) 
+Gecko/20061201 Firefox/2.0.0.3 (Ubuntu-feisty)"
217.0.22.3 - - [10/Apr/2007:10:54:53 +0300] "GET /cgi/pti.pl HTTP/1.1"
+ 500 617 "http:/contact.local/" "Mozilla/5.0 (X11; U; Linux i686; en-
+US; rv:1.8.1.3) Gecko/20061201 Firefox/2.0.0.3 (Ubuntu-feisty)"
127.0.0.1 - - [10/Apr/2007:10:54:08 +0300] "GET / HTTP/0.9" 200 3700 "
+-" "Mozilla/5.0 (X11; U; Linux i686; en-US; rv:1.8.1.3) Gecko/2006120
+1 Firefox/2.0.0.3 (Ubuntu-feisty)"
217.0.22.3 - - [10/Apr/2007:10:58:27 +0300] "GET / HTTP/1.1" 200 3700 
+"-" "Mozilla/5.0 (X11; U; Linux i686; en-US; rv:1.8.1.3) Gecko/200612
+01 Firefox/2.0.0.3 (Ubuntu-feisty)"
217.0.22.3 - - [10/Apr/2007:10:58:34 +0300] "GET /unix_sysadmin.html H
+TTP/1.1" 200 3880 "http://pti.local/" "Mozilla/5.0 (X11; U; Linux i68
+6; en-US; rv:1.8.1.3) Gecko/20061201 Firefox/2.0.0.3 (Ubuntu-feisty)"
217.0.22.3 - - [10/Apr/2007:10:58:45 +0300] "GET /talks/Fundamentals/r
+ead-excel-file.html HTTP/1.1" 404 311 "http://pti.local/unix_sysadmin
+.html" "Mozilla/5.0 (X11; U; Linux i686; en-US; rv:1.8.1.3) Gecko/200
+61201 Firefox/2.0.0.3 (Ubuntu-feisty)"
[download]

Output:

127.0.0.1 => 8
139.12.0.2 => 2
217.0.22.3 => 6
Number of unique IPs: 3
[download]

If you're not interested in the count for each IP, you can just use $hash{$1} = 1 instead of incrementing. Either way, the keys will contain log file's unique IPs. Regexp::Common is used in capturing the IPs.