A couple of advices :

• for($i=0; $i<=$length; $i++){ isn't very perlish; you could use foreach my $url (@list) { instead.
• You'd better use open(...) or die "...". It doesn't matter with open but in many cases || gets precedence over other operators and cause your program to fail unexpectedly.
• Well actually, you don't really need looping twice, once to read the file, and twice to get the url; you could easily do it all in the same loop.

So we could have:

#!/usr/bin/perl

use strict;
use warnings;
use LWP::Simple;

my $counter=1;
my $file="C:/Documents and Settings/Dad/Desktop/url checker.txt";

open FILE, "<$file" 
    or die "Can't open the list of urls! \n";

while(<FILE>){
    my $source=get($_);
    open LOG, ">C:/Documents and Settings/Dad/Desktop/Websites/Website
+ Source $counter.txt" 
        or die "Can't open website sources.txt: $!\n";
    print LOG $source;
    close LOG;
    $counter++;
}

close FILE;
close LOG;
[download]

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