if (( defined $buf ) || ($buf =~ /\w/))

##</code><code>##

if (( defined $buf ) && ($buf =~ /\w/))

##</code><code>##

your server with my modification:
use IO::Socket;
use IO::Select; 
use strict;

my ($server, $client, $buf, $new_sock);
my ($SOCK_STREAM, $server_port); #pg: remove $buf, defined twice.

{

	my $listener=IO::Socket::INET->new( LocalPort => 21000, Listen => 2, Reuse => 2 );
    	die "Can't create socket for listening: $!" unless $listener;
    	print "Listening for connections on port 21000\n";
    
    	my $readable=IO::Select->new;      
    	$readable->add($listener);         

    	while(1) 
    	{
        	my ($ready) = IO::Select->select($readable, undef, undef, undef);
        	foreach my $s (@$ready) 
        	{   
				if($s == $listener) 
				{
        			$new_sock = $listener->accept;	
        			$readable->add($new_sock) if $new_sock;   	
        			print $new_sock "Welcome!\r\n";                        			
        		} 
        		else 
        		{  
        			print $listener "Why don't you call me anymore?\n";
        			
        			$buf = <$s>;   
        			print "$buf" if (defined($buf)); #pg: added if defined
        			
        			if (( defined $buf ) && ($buf =~ /\w/)) #pg: it was ||
        			{          
        	            		if ($buf =~ /goodbye/i) 
        	            		{
        	                		print $s "See you later!\n";
        	                		$readable->remove($s);
        	                		$s->close;
        	            		} 
        	            		else 
        	            		{
        	                		print $s "You said: $buf\n";
        	            		}                  
	
		                } 
		                else 
		                { 
		        		print $new_sock "Still there?\r\n";
			                $readable->remove($s);
        	            		$s->close;
        	            		print STDERR "Client Connection closed, because you said $buf\n" if (defined $buf); #pg: added checking for defined $buf
        	        	}
        	    	}
		}
    	 }

}

your client with my modification:
use Socket;
use IO::Socket;
use strict;
my ($remote_host, $remote_port);
my ($internet_addr, $paddr);
my ($soc, $answer, $socket);

{
	use IO::Socket;
	
	$remote_host="localhost";
	$remote_port=21000;
	
	$socket = IO::Socket::INET->new(PeerAddr => $remote_host,
	                                PeerPort => $remote_port,
	                                Proto    => "tcp",
	                                Type     => SOCK_STREAM)
	or die "Couldn't connect to $remote_host:$remote_port : $@\n";

	
	do
	{
		print $socket "New host\n";	
		$answer=<$socket>;	
		print $answer;
	}while ($answer !~ /end/); #pg: was =~, it shall really be !~
	
	close($socket);
}