A slight mod to BrowserUk's code is what you need:

#!/usr/bin/perl -w
use strict;

open ONE, '<', "one.txt" or die "First File: $!\n";
open TWO, '<', "two.txt" or die "Second File: $!\n";

until( eof( ONE ) and eof (TWO)) 
{
    my $one = <ONE>;
    my $two = <TWO>;
    $one ||= "";
    $two ||= "";
    chomp($one);
    chomp($two);
    print "$one\t$two\n";
}
__END__
OUTPUT:
a   this is
0   file two
ab  
dsf 

one.txt:
a 
0
ab  
dsf

two.txt:
this is
file two
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