One fairly efficient way is to count newlines in the file. The following program uses a feature of tr///, as documented in perlop. If your text file doesn't end with a newline, then it's not really a proper text file, so this may report one fewer line than you expect.
$lines = 0; open(FILE, $filename) or die "Can't open `$filename': $!"; while (sysread FILE, $buffer, 4096) { $lines += ($buffer =~ tr/\n//); } close FILE;This assumes no funny games with newline translations.