You can use Term::ReadKey for that.

Update: In its most simple case, this could be something like

use Term::ReadKey;

ReadMode 'noecho';
my $passw = ReadLine;
ReadMode 'restore';

print "$passw\n";  # just to check
[download]

Or, if you want to use the console/tty instead of STDIN — which would keep people from piping in passwords (like echo foo | perl 758036.pl):

use Term::ReadKey;
use Fcntl "O_RDWR";

if ($^O =~ /Win32/i) {
    sysopen IN, 'CONIN$', O_RDWR or die "Unable to open console for in
+put: $!";
} else {
    open IN, "<", "/dev/tty" or die "Unable to open tty for input: $!"
+;
}

ReadMode 'noecho', *IN;
my $passw = ReadLine 0, *IN;
ReadMode 'restore', *IN;

print "$passw\n";  # just to check
[download]

Or, yet another version with rudimentary editing capabilities (backspace):

use Term::ReadKey;
use Fcntl "O_RDWR";

if ($^O =~ /Win32/i) {
    sysopen IN, 'CONIN$', O_RDWR or die "Unable to open console for in
+put: $!";
} else {
    open IN, "<", "/dev/tty" or die "Unable to open tty for input: $!"
+;
}

ReadMode 'noecho', *IN;

my ($ch, $passw);
do {
    $ch = ReadKey 0, *IN;
    $passw .= $ch;
    substr($passw,-2)='' if ord($ch)==127; # BS
} until ($ch eq "\n");

ReadMode 'restore', *IN;

print "$passw\n";
[download]