wget as moritz suggested will definitely work. If you need to do it in a Perl program, you can try LWP.

use LWP;
$have = length($file);
$response = $ua->get($URL,
'Range', "bytes=$have-");
[download]

#!/usr/bin/perl --

use strict;
use warnings;

use LWP;
use File::Slurp qw' read_file write_file ';
use File::Spec;

Main(@ARGV);
exit(0);

sub Main {
    my $mech = LWP::UserAgent->new;

    my $ua = $mech;
    $ua->add_handler( "request_send",  sub { shift->dump; return } );
    $ua->add_handler( "response_done", sub { shift->dump; return } );

    my $file = File::Spec->rel2abs(__FILE__) . '.temp.html';

#~     print "$file \n";

    write_file( $file, ( '#' x ( 5810-9 ) ) );

    $ua->resume( 'http://www.cpan.org/', $file );

    print "----\n",substr( read_file( $file ), -20 ), "\n\n";

    unlink $file;

} ## end sub Main

sub LWP::UserAgent::resume {
    my ( $self, $uri, $file, @rest ) = @_;

## TODO: Accept-Ranges
## TODO: If-Range
## TODO: If-Unmodified-Since
## TODO: Last- Modified

    eval {
        $uri = $uri->url if ref($uri) eq 'WWW::Mechanize::Link';
        $uri = $self->base ? URI->new_abs( $uri, $self->base ) : URI->
+new($uri);
    };

    open my ($fh), '>>', $file or die "Can't open '$file' for append: 
+$!";
    binmode $fh;

    @rest = (
        ':content_cb' => sub {
            my ( $data, $response, $protocol ) = @_;
            print $fh $data;
            return;
        },
        @rest
    );

    my @stat = stat($fh);
## 9 mtime

    require HTTP::Request::Common;
    my @suff = $self->_process_colonic_headers( \@rest, 0 );
    my $req = HTTP::Request::Common::GET( $uri, @rest );

    $req->headers->header( Range => 'bytes=' . $stat[7] . '-' );
    @rest = $self->request( $req, @suff, @rest );

    close $fh;
    return @rest;
} ## end sub LWP::UserAgent::resume


__END__
GET http://www.cpan.org/
Range: bytes=5804-
User-Agent: libwww-perl/5.837

(no content)
HTTP/1.1 206 Partial Content
Connection: close
Date: Sat, 02 Oct 2010 01:39:24 GMT
Accept-Ranges: bytes
ETag: "61c606-16b2-491805f445dc0"
Server: Apache/2.2.14 (Unix)
Content-Length: 6
Content-Range: bytes 5804-5809/5810
Content-Type: text/html; charset=ISO-8859-1
Last-Modified: Thu, 30 Sep 2010 21:00:47 GMT
Client-Date: Sat, 02 Oct 2010 01:40:23 GMT
Client-Peer: 207.171.7.177:80
Client-Response-Num: 1

(no content)
----
###########
</html>
[download]