Freestanding subwoofers are the most popular choice for home cinema systems. They provide good performance, flexible positioning and value for money. The size of the subwoofer should generally match the size of the space it needs to fill, but bigger subs with larger drivers and greater cabinet volume do produce lower frequencies, so typically bigger is better. For ultimate bass performance multiple subwoofers are often used.
Active subwoofers with built-in amplifiers are by far the most common type of freestanding subwoofer. An active subwoofer can be connected directly to the output of a compatible amplifier to provide the all important LFE (Low Frequency) channel for home cinema, or to add bass performance to 2-channel music systems.
Passive freestanding subwoofers are less common, but are sometimes used in high performance systems that require multiple subwoofers or specific amplification.
If it's undesirable or not possible to position a freestanding subwoofer in the room, then why not consider a discreet in-wall or in-ceiling subwoofer.