You must have a subwoofer for real home-theater sound
No — and yes.
If the main left/right speakers produce true deep bass with minimal attenuation to below 30 Hz — and money, space, or both are in short supply — then no. But where both are available in surplus, any home theater system will be improved by introducing a true subwoofer, one that extends response through the lowest octave, and/or enhances dynamic potential there, while offering more equal bottom-octaves playback thanks to the freedom to place a sub as room acoustics dictate.
