Well the perfect credit score is 850 but it seems that the worst possible credit score is only 300.
Even so, apparently it is rather difficult to get a 300, you have to hit bottom in every single category and then probably go back and do it again. However, it is highly doubtful that many people aspire to that goal.
You can, however, not qualify for a credit score and therefore not have one, since it takes 6 months after you open an account for it to be reported. But the way that usually happens is that you go from no score at all to a decent score.
Credit scores have been dipping though and very few people ever get to close to that 850 score either.
Read ?How Low?.