I would look for a variety of factors in a good subwoofer, but I would have to go with low-end extension and low distortion (with SPL and footprint size as two other important considerations).
Clean low end extention is absolutely the most important attribute for a good sub. The ability to shake the house is the thing that makes movies worth watching!
I voted for 4 of them by accident, however I feel they are all important and tied together.
Low end extension is not possible without minimal compression effects nor is it usefull without low distortion. Tactile response requires low distortion output to make it worth while. A good subwoofer requires many aspects to make it a great package. All of those are important to me.