Ummm... You're actually close, although you're off by 1. Fencepost error - you're terminating the loop one too early, so you're not including 1e6 in the loop. When in doubt, let perl figure out the right way to do it for you:

A slightly modified version:

#!/usr/bin/perl -w

use strict; # or die :-)

my $LIMIT = 1000000;

my $s;

foreach (1 .. $LIMIT) {
    foreach (/./g) {
        $s += $_;
    }
}

print "Sum: $s\n";
[download]

Golfers invited to make this even nicer (not to mention make it run faster...)