The answer to this question is fairly simple. Do you need strong, stable, steady support under your mattress? Yes. Does it have to be a box spring? No, absolutely not!
Box springs have lost most of their original function over the years. That's the reason we can get away with putting mattresses on things like adjustable bases or metal platforms now instead of relying on box springs. There was a time when box springs were the literal “spring” in your mattress. They were a necessary part of the comfort of your bed. Over the years, we have gotten better and better at manufacturing mattresses. Now we're able to get those springs into the actual mattress, making the mattress unit as a whole more useful, comfortable, and durable. Because of this, you will hear mattress retailers and salesmen refer to box springs as simply “foundations.” This term is more accurate than “box spring” because these days, the sole purpose of a bed foundation is much like a house foundation: to provide strong support and structure.
This being said, not all box springs are created equal. Some are simply wooden frames while others are made of steel, making them far more durable and less prone to squeak. For a quick overview of some of the box springs on the market right now, you can check out this article
Your choices are not limited to box springs anymore. For most mattress warranties, some sort of foundation is required . This is one of many reasons not to put your mattress directly on the floor. Adjustable bases and platforms are becoming more and more popular as traditional box spring replacements. Adjustable bases and platforms usually fit warranty parameters and are superior to box springs in just about every way. Adjustable bases are in a class of their own as far as price and quality of sleep. High quality platforms, however, are generally about the same price as a box spring and frame combo and last at least twice as long.