The most important component of a home theater depends upon the person, equipment, budget and space everything is set up in, including seating, lighting, flooring, etc. Here are components carrying the most importance.
Location
Left to chance, the set up on the entire home theater system and area could be chaotic. For example, there needs to be room for the projector to show on the screen without interference from anything (high furniture, misplaced lights, etc.) Not to mention, if the main theater viewing screen is not the focal point of the room, many guests will not be able to view anything well, there could be a lack of seating for the right gaming and other screens, quarters could be cramped, remotes and other tools and minor equipment disorganized resulting in not much fun!
Needs Met
Likewise, if family needs are left to chance, chaos could rain. Lets say the family budget is a bit tight. The teenagers all have an Xbox console, compatible gaming accessories and games (hence the budget is tight now). Everything is purchased, assembled, placed, up and running. And oops, you realize your wife bought a Playstation instead of an Xbox 360. Could be...