Truncating just the superfluous newlines should work, too.  This would avoid rewriting the entire file, and/or reading it into memory.

open my $fh, "+<", $fname or die $!;

my $pos = (-s $fh) - 1;
my $s;
do {
    seek $fh, $pos--, 0;
    read $fh, $s, 1;
} while $s eq "\n";

truncate $fh, $pos + 3;
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(On Windows you'd need to truncate at $pos + 4, or else you'd have just a trailing \r, not a complete \r\n.)

Update: ww remarked via /msg that on Windows ActiveState Perl < 5.14, truncate only works on closed files (according to his tests), but that as of 5.14(.2) it does behave as expected.   I don't have Windows here to verify, so I can only pass this on as is.   Thanks anyway!

The first part of the trick is to 'slurp' the file. Set the special variable $/ to undef to read the entire file in one hit:

use strict;
use warnings;

my $file = <<FILE;
1
2
3


FILE

open my $fIn, '<', \$file;
my $str = do {local $/; <$fIn>};
close $fIn;

print "1-->\n$str<--1\n";
$str =~ s/\n+\Z//;
print "2-->\n$str<--2\n";
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Prints:

1-->
1
2
3


<--1
2-->
1
2
3<--2
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What have you tried so far?

When you read an empty line, you can't know yet whether to print it. So you need something along the lines of

my $newlines = 0;
while (<$file>) {
    if (/^$/) {
        $newlines++;
    }
    else {
        print "\n" x $newlines;
        print;
        $newlines = 0;
    }
}
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(untestested).

update: closed regex, ww++.

use Tie::File;

foreach my $filename (grep { -f } @ARGV) {

    print "** Processing $filename\n";

    tie my @file, 'Tie::File', $filename
      or die "Unable to tie: $!\n";

    pop @file while $file[-1] eq q{};

    untie @file
        or die "Unable to untie: $!\n";

    print "** Done...\n\n";
}
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perl -ne'$b.=$_;/./||next;print$b;$b=""' your-file
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Brilliant !!

See also flip, dos2unix, etc.

perl -0pe '~s/\n+$/\n/' your-file
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