You could put a simple waitpid call in your while loop there, just to hang around while there's still a kid out there. I didn't even need the POSIX module:

while ($forked > 0) {
    print "[$forked] ";
    last if (waitpid(-1,0) == -1);
    sleep 1;
}
[download]

That's not a beautiful solution, though. Here's another attempt:

#!/usr/bin/perl -w

use strict;
$|=1;

my %kids;
$SIG{CHLD} = \&REAPER;          # set handler for fork

for (1..10) {
    my $pid = fork();
    die "Fork failed" unless defined $pid;
    if ($pid == 0) {
        print "Hello $$\n";
        sleep 1;
        print "Bye $$\n";
        exit;
    } else {
        $kids{$pid} = 1;
        print "Started child $pid\n";
    }
}

foreach my $kid (keys %kids) {
    print "Waiting for [$kid]:\n";
    my $val;
    do {
        $val = waitpid($kid, 0);
    } until $val == -1;
    delete $kids{$kid};
}

print "Done\n";
exit;

sub REAPER {
    my $pid = wait;
    $SIG{CHLD} = \&REAPER;      # reinstall for sysV (not needed)
    print "Finished child process $pid" . ($? ? " with exit $?" : "") 
+. "\n";
    delete $kids{$pid};
}
[download]

Not perfect, but you get the chance to be more specific on what you're waiting for.