How can I make my hash remember the order I put elements into it?

Use the Tie::IxHash from CPAN.

    use Tie::IxHash;
    tie(%myhash, Tie::IxHash);
    for ($i=0; $i<20; $i++) {
        $myhash{$i} = 2*$i;
    }
    @keys = keys %myhash;
    # @keys = (0,1,2,3,...)