If this question is meant literally, I'm sure other forms or substances could be used to clean a person's teeth. Dental mouthwashes include anti-plaque substances to fight cavities; sugar-free gum helps to eliminate food particles; and a dental pick or some other form of substitute for the brush (dental floss, dental strips) would suffice if the brush was competely outlawed.
Of course you could find some other way to keep your teeth clean, but teeth health is very important. Tooth decay is caused by bits of tartar that build up on your teeth. If the tartar builds around your gums, it can also lead to gingivitis.
Anyone can live without a toothbrush. Of course good dental higeine would be more difficult to achieve, but it is possible. Consider the day and age before the toothbrush was invented. At one point people would crush the end of twigs causing them to splinter into shreds, and then they would use the shredded end to scrub at their teeth.
Yes and many are still living without tooth brush with as good an oral hygiene as can be achieved with tooth brush as mentioned by Ask96. Many Muslims use twigs of medicinal plants/trees for cleaning their teeth according to their tradition. As a matter of fact tooth decay has more to do with the life style and eating habits. Candies, chocolates and soft drinks are the main reason for the tooth decay due to their sugar content and acidic behavior respectively. In older times people consumed fruits and purer fibrous foods at fixed timings. Foods included higher fiber content help cleaning and a glaring example is the use of whole grain floor as compared to fine white floor. All these life style changes have adversely effected the oral hygiene.