Summarize:

Not all theaters will require the same formality of dress. Pay attention to what kind of production you'll be attending and decide the most appropriate way to dress. For instance, it's improbable that a production aimed for children will require any particular fashion sensibilities, whereas attending even a small, locally produced opera might make you want to consider nicer wardrobe choices. In this case it's all about context. Special black tie events and opening nights will usually call for formal attire, while you should feel free to dress casually for the average Broadway or matinee show, or for more conceptual dramas like those put on by black box theaters.  It can be a good idea to run a search or call up the theater managers before a show to find out whether there is an expected dress code. If you're ever uncertain about what to wear to a given event and have no guidelines to follow, it's usually alright to go casual. If you've seen the show before, or if a merchandise booth is selling souvenirs before the show, grab a t-shirt or hat to show your support. Many long-running or family oriented shows appreciate when fans show up wearing that production's apparel. These products are often unique and exclusive to that live performance, so you'll never have a better chance to model them. This is a no-no for most opening nights and more focused productions, but for established shows like The Lion King and Wicked it is encouraged and can be a lot of fun, especially for younger kids. Dress yourself or your child up as your favorite characters and have fun immersing yourself in the event. Just don't go too overboard with costumes and props—remember, an audience member's appearance can be distracting. Do some research to find out whether a particular show recommends the use of costumes and props before you buy your tickets and decide what to wear. Even then, keep elaborate costumes reasonable and don't be tempted to act out or make noise during the show. In rare instances it may be okay to come as you are. Off-Broadway shows and smaller productions usually don't mandate a dress code, so jeans and sneakers won't be an issue. Make sure you always know ahead of time what the expected mode of dress is for a given production or venue, and enjoy an increasingly uncommon opportunity to present yourself fashionably at a formal society event. Even if normal clothes are allowed, it's never a bad idea to dress nicely. Your appearance says something about your character, so make sure it has good things to say.
Know what is expected. Buy and wear merchandise. Put on costumes and facepaint. Wear everyday clothes.