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Adding milk to a dough is, most of the time, a consideration of adding liquid to a dough in order to avoid a dry end product[^1]. Baked goods tend to be exposed to high heat for a prolonged time so that a dough should be properly "hydrated" so that you get a crunchy and soft result.

The other answers already provided good alternatives. Some other alternatives include:


 * Plain water
 * Juices (mixed with water or pure)
 * Alternative milk-based product (like the already mentioned soy milk but also oat milk, almond milk, rice milk, etc.)
 * Mixing milk derivates with water (not what was asked for but for listed for completeness)

A few advantages with these alternatives is that you can adjust the flavour of the final product. For example, I like to add some apple juice in my bread doughs so that the breads have a slight taste of apples and are more "fruity". (I like apples a lot!) Using water as a replacement leads to a "cleaner" taste as the it doesn't obfuscate the taste of the other ingredients which were used.

So basically: add liquid to your dough, which kind can usually be ignored[^2].

[^1]: As @dsr pointed out, milk is primarily water and some other things (protein, fat, sugar). When adding small amounts of milk, the other parts of the milk usually can be neglected, especially in comparison to the amounts you use anyway as part of the recipe. They do help but missing them will most of the time not change the taste to a degree that it would be noticeable.
[^2]: If doing a recipe that uses a lot of milk in comparison to other recipes (for example 1:1 with other ingredients), one should notice that the part about using a lot of milk might be the very reason why the recipe is the way it is, so substitution isn't very suitable anyway.