Given the range of permissible widths by the tire manufacturers, there's not a "one size fits all" answer to this question.
For example, Schwalbe tires up to 2.4, VEE up to 2.35 and Maxxis tires up to 2.5 WT will work. In the case of the Frechdax, Dreckspatz and Bam Bam kids bikes, we recommend that using the widths of the factory-fitted tires.