Late to reply because this is a tough question.
1) I lean toward lean bass as a preference. (Likely because so many subwoofers seem slow on the uptake.) So,
first, is speed of the woofer/subwoofer, no matter how low I wanna go. (I think SVS does a good job, and I have some Genesis servo woofers that can keep pace in a good way. I also use some old Acoustat 2+2 speakers as woofer only and they are speeee-dy!)
2) More than thumping the house, I think a good woofer adds atmosphere and 'air,' which might sound nuts, but it really seems to enhance spatial cues and sense or 'place.' Woofers that make it into the 35-40 Hz range start to achieve this, so that would be my minimum in terms of the question.
3) The main speakers has to be able to handle dynamic transients at higher frequencies to really make things work. Bass transients come with a lot more than just bass frequencies, so the main speakers need to be stout enough to work with the woofer, as well.
4) I think there is ample bass content into the 20 Hz range that makes reproducing those sounds very worthwhile. It can add 'emotion' to how the music impacts me and enhances the soundstage. (Subjectively speaking, I don't know how an objectivist would feel about my listening impression. So, take this is as worthless subjective listening feelings.)
All that adds up to a vote for a deep reaching woofer. If you are going to to do it, do it well! Plus, great fun playing with placement and settings....adjustability is another important part. To sum up, how deep? "Balls deep, but fast."