Here's my uber-inelegant serialized approach... If you don't care about the order that every combination is created: (btw, I renamed @array to be @arrays)...

my ($carry, @tallykeeper) = map 0, @arrays, 0; #gets rid of warnings..
+. w/strictures
while (!$carry) {
   $carry = 1;
   for my $dx (0 .. $#arrays ) { 
      print $arrays[$dx]->[$tallykeeper[$dx]]; 
      $tallykeeper[$dx] += $carry;
      if ($tallykeeper[$dx] < @{$arrays[$dx]}) {
          $carry = 0;
      }else{
          $tallykeeper[$dx] = 0;
      }
   }
   print "\n";
}
[download]

OR if you MUST have it in that order you could reverse the order of your array lists, or with my solution use this solution:

my ($carry, @tallykeeper) = map 0, @arrays, 0; #gets rid of warnings..
+.
while (!$carry) {
   $carry = 1;
   my $combostr = ""; 
   for my $dx (reverse 0 .. $#arrays ) { 
      $combostr .= $arrays[$dx]->[$tallykeeper[$dx]]; 
      $tallykeeper[$dx] += $carry;
      if ($tallykeeper[$dx] < @{$arrays[$dx]}) {
          $carry = 0;
      }else{
          $tallykeeper[$dx] = 0;
      }
   }
   $combostr = reverse $combostr;
   print "$combostr\n";
}
[download]

Okay mine are ultra lame... but it was fun to try to make a generic solution that worked for everything possible array of arrays...

--Ray