You could use a recursive permute function:

sub permute{
  my ($prefix,$c,@arrays)=@_;
  my @ret=();
  foreach(@$c){
    my $f=$prefix.$_;
    if(scalar(@arrays)==0){
      push @ret,$f;
    }else{
      push @ret,@{permute($f,@arrays)};
    }
  }
  return \@ret;
}

my $perms=permute('',['C','A','T'],['D','O','G'],['B','I','R',D']);
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this is a bit slower than the standard nested-loop approach, but it has the advantage that it is generic and you don't need to alter your code if you have more lists. (btw, I seem to remember merlyn having a similar, but much slicker permute function that does more or less the same thing lying around somewhere)