No less than eight levels above
I generally don't read deeply nested comments (except when I load the Recent Comments page, which shows me everything without knowing how deep it is). I find they're rarely worth it, especially when it's just two people going hammer and tongs at each other. Even if one of the two people is me.
I just found out that a new website feature was implemented 2 days ago. If a comment is voted to -4 or below, it and all replies and downstream comments from it will be hidden from Recent Comments, and further replies in that subthread will incur 5 karma points penalty. The hiding, but not karma penalty, applies retroactively to comments in that subthread posted before the -4 vote.
This seems to be worth a discussion post since most people are probably still voting things to below -3 without knowing the new consequences of doing so.