Your second open for the writing is clobbering the contents of your "report.txt" every time you go through the list of words so it's only going to contain the last word from the last line in "file.txt". You probably want to move that open outside the outer while loop (as well as adding error checking to opening "file.txt" for reading but that's another story).

Edit: Additionally if you formatted things better it'd be clearer what your code is doing and you might could see where the problem is more easily.

Edit again: Meh, fish.

my $infile  = q{file.txt};
my $outfile = q{report.txt};

open(my $in_fh,  q{<}, $infile ) or die "Couldn't open '$infile' for r
+eading: $!\n";
open(my $out_fh, q{>}, $outfile) or die "Couldn't open '$outfile' for 
+writing: $!\n";

while( <$in_fh> ){
  chomp;
  my @words = split( q{ } );
  for my $word (@words) {
    print $out_fh "$word\n";
  }
}
close( $in_fh );
close( $out_fh );
print "done\n";
[download]

What's going wrong is that the open mode > clobbers the output file. Although you could use >> to append to the file, opening it on every iteration of the loop is pretty inefficient, and so Fletch's suggestion of moving the open outside of the loop is better.

You should also definitely always Use strict and warnings, and apply the advice from "open" Best Practices to all of your opens.