m/(\w+)\s+$c\s+/ won't work because of cases like this:

Mexico is my favorite country.
I like Mexico.
Welcome to Mexico--a fun place.
[download]

You need a negative look-behind for excluding 'New Mexico' (see perlre), and in general I suggest just having a list of regex's to check against:

my @countries = (  # make a list of regex's
  qr/(?<!New )Mexico/,
  'France',
  'Germany',
  qr/(?:(?:U\.S\.(?:A\.)?)|USA?|(?:The )?United States(?: of America)?
+)/,
);
my $s = do {local $/=undef; <DATA>};
my %found;
foreach my $re ( @countries ){
  $found{$1}++ while $s =~ s/\b($re)\b/====/s;  # NOTE: this is destru
+ctive to $s, but does get us the counts.
}
use Data::Dumper;
print Dumper \%found;
__DATA__
Mexico is my favorite country.
I like Mexico.
Welcome to Mexico--a fun place.
New Mexico
US France Germany
U.S.A.
USA
U.S.  US
United States
United States of America
The United States
The United States of America
[download]

Hmm.. /me thinks i should add making a Regexp::Common::Country module to my project list