The rules for taking children to the theater can vary with each production, but if we're talking about a Broadway, off-Broadwy or regional theater production aimed at adults, you should not take children 4 years old or younger to the show.
For children older than that, check the show's website, and there will typically be an advisory for appropriate ages.
Regardless of the venue, some shows are designed for children and appropriate for all ages. Again, the show's website should make that clear.
Regardless of the advisory, it's important that you know what your child can handle. As an example, the advisory on Hair is "mature," but you would be allowed to take a pre-teen. You need to know if the nudity and frank depictions of sex and drug-taking are appropriate for your family.
