Many seemingly unrelated protein families share common folds. Theoretical models based on structure designability have suggested that a few folds should be very common while many others have low probability. In agreement with the predictions of these models, we show that the distribution of observed protein families over different folds can be modeled with a highly-stretched exponential. Our results suggest that there are approximately 4,000 possible folds, some so unlikely that only approximately 2,000 folds existing among naturally-occurring proteins. Due to the large number of extremely rare folds, constructing a comprehensive database of all existent folds would be difficult. Constructing a database of the most-likely folds representing the vast majority of protein families would be considerably easier.