You can use Tac (Unix) if you are on a Unix like operating system. It's much faster than using Perl and File::ReadBackwards:

# ls -lh /var/lib/mysql/ibdata1
-rw-rw----  1 mysql mysql 66M Mar 19 11:05 /var/lib/mysql/ibdata1

# wc -l /var/lib/mysql/ibdata1
323833 /var/lib/mysql/ibdata1

# time tac /var/lib/mysql/ibdata1 > /tmp/bar
real    0m0.643s
user    0m0.173s
sys     0m0.322s

# time /usr/bin/perl > /tmp/foo
use warnings;
use strict;
use File::ReadBackwards;
my $bw = File::ReadBackwards->new( '/var/lib/mysql/ibdata1' ) or
  die "$!" ;
while( defined( my $log_line = $bw->readline ) ) {
  print $log_line ;
}
__END__
real    0m29.076s
user    0m11.910s
sys     0m10.819s

# md5sum /tmp/foo
2b31d9f47525853842d5dbce584bd95c  /tmp/foo
# md5sum /tmp/bar
2b31d9f47525853842d5dbce584bd95c  /tmp/bar
[download]

Update Wed Mar 26 10:05:03 CET 2008: Added number of lines in input file.

Update Wed Mar 26 10:11:31 CET 2008: It seems that the tac + process file forwards using Perl approach combined is still much faster than process file using Perl and File::ReadBackwards:

# time /usr/bin/perl > /tmp/foo
use warnings;
use strict;
use File::ReadBackwards;
my $bw = File::ReadBackwards->new( '/var/lib/mysql/ibdata1' ) or
  die "$!" ;
while( defined( my $log_line = $bw->readline ) ) {
  $log_line =~ s/1/2/g;
  print $log_line;
}
__END__

real    0m27.431s
user    0m12.906s
sys     0m10.701s
[root@afflinux aff]# time /usr/bin/perl > /tmp/bar
use warnings;
use strict;
my $FH = undef;
open($FH,  '/var/lib/mysql/ibdata1' ) or
  die "$!" ;
while( my $log_line = <$FH> ) {
  $log_line =~ s/1/2/g;
  print $log_line;
}
__END__

real    0m5.249s
user    0m1.535s
sys     0m0.293s
[download]