What are the standard properties of an S-Box Apart form the following, what are the other properties of a good cryptographic Substitution box or the S-Box:


Changing one input bit should change about half of the output bits.
Each output bit should depend on every input bit.
Another very common criteria for an S-box with $n$ input bits and $m$ output bits with $m\le n$ (as most commonly used S-boxes are) is that each of the $2^m$ output values should be reached for exactly (or at least near) $2^{n-m}$ input values.

The question's criterion 1 can be made strict and become the Strict Avalanche Criterion. There are even stricter /higher-order versions. There also is the Bit independence criterion. The desirability of these properties depends on the overall design of the cryptographic construction using the S-box, and is not easy to assess.

More generally, S-boxes are typically optimized with use as part of a particular cryptographic construction in mind, aiming at improving it's overall resistance against cryptanalytic attacks, as pointed in comment.