Without a doubt, low end extension with low distortion. I've gone and listened to peoples setups with one of those HTIBs that claim to have a sub but only reach down to 35 or 40 Hz. Then I have them go listen to a system that can hit 20 with the same material. Almost always I get the comment "I didn't know what I was missing".
That, exactly, is what a good sub should do for a system. I love high SPLs as much as the next basshead but the reality of my family life is such that I rarely listen at or near reference levels. A good sub should be able to produce convincing results without my reciever turned up to "11".
Looks are nice, but only to the degree that my wife doesn't reject it, past that point I rarely use a sub as a display piece of furniture. I know those that would disagree and have rooms where they "showcase" the looks of their system, but on a reasonable budget of $400-$800 for a sub I'd rather have the money spent toward sound than looks.
I'm not even certain what "tactile response" means - does this refer to room shaking or musicality?
Ok, SVS, make my Christmas merry!