#! /usr/bin/perl
# ----------------------------------------------------
$mailprog = '/usr/sbin/sendmail';
$cuenta = 'inscripciones@ceadmex.org';

# Get the Date for Entry
$date = `date +"%A, %B %d, %Y at %T (%Z)"`;
        chop($date);
$shortdate = `date +"%D %T %Z"`;
        chop($shortdate);
# Get the input
read(STDIN, $buffer, $ENV{'CONTENT_LENGTH'});

# Split the name-value pairs
@pairs = split(/&/, $buffer);
foreach $pair (@pairs)
{
    ($name, $value) = split(/=/, $pair);


    $value =~ tr/+/ /;
    $value =~ s/%([a-fA-F0-9][a-fA-F0-9])/pack("C", hex($1))/eg;

    $FORM{$name} = $value;
}
# Alta a variables
use CGI qw/:standard/;

$EMPR = param('empr');
$APPA = param('appa');
$APMA = param('apma');
$NOMB = param('nomb');
$EMAL = param('emal');
$TELE = param('tele');
$DIRE = param('dire');
$COLO = param('colo');
$CIUD = param('ciud');
$ESTA = param('esta');
$PAIS = param('pais');
$COPO = param('copo');
$CURS = param('curs');


################# Mandar Correo ############
 open (MAIL, "|$mailprog $cuenta") || die "Can't open $mailprog!\n";
 print MAIL "From: $EMAL\n";
 print MAIL "Subject: DATOS\n\n";
 print MAIL "--------------------------------------\n";
 print MAIL "DATOS DE LA PERSONA\n";
 print MAIL "Nombre: $NOMB $APPA $APMA\n";
 print MAIL "Direccion: $DIRE $COLO $CIUD $ESTA $PAIS $COPO\n";
 print MAIL "-----------------------------------\n";
 print MAIL "DATOS DE LA RETROALIMENTACION\n";
 print MAIL "EMPRESA: $EMPR $TELE\n";
 print MAIL "CURSO" $CURS\n";
 print MAIL "---------------------------------------\n";
 print MAIL "-----------------------------------\n";
 print MAIL "FECHA Y HORA DE ESTE FORMATO\n";
 print MAIL " - $date\n";
 print MAIL "---------------------------------------\n";
close (MAIL);
[download]

Let's start with some thoughts on your code:
• First, use strict and use warnings. It will save you a lot of headaches in the long run; you will have to declare all your variables (with my, probably)
• Second, don't use a system call to get the date; use localtime() instead (see `perldoc -f localtime`).

Apart from that, I really don't see anything weird about your code. How are you testing it and how are you compiling it?