As evidenced by the poll results, to most people (including myself), deep, accurate, powerful reproduction is key to a successful home theater sub. The lowest octaves, 20 Hz or even slightly lower, are a key part of a true home theater experience, along with the power and build quality to rumble your room WITHOUT distortion. Accuracy (flat frequency response as well as clarity without overhang or boom) is very important to produce a natural sound that accurately reproduces what's on the DVD soundtrack. A sub with these qualities will sound very musical too on either movie soundtrack music or 2-channel music from CD or multichannel audio.
Aesthetics of course are important depending on the customer; I personally don't care if it's a big black box or a beautifully finished wood veneer cabinet, but some folks do care. To me a beautiful box is useless if it doesn't sound outstanding.
Features too are a consideration; speaker-level inputs with crossover, phase controls, built-in parametric EQ, defeatable auto-on control, variable tuning via switches and port plugging... These things can all lend to the attraction of a subwoofer product. But again, all worthless without the SOUND.