A Call for Armchair Miss Manners-ing: Overstaying Your Welcome

TH has assured me that I'm not overstaying my welcome here at Trailheadcase. She has the green light to kick me out anytime, though, and she knows it.

Nevertheless, I do have a serious question about overstaying one's welcome or, more generally, about when to draw the line on taking advantage of the goodwill of friends or family.

Say you have to travel to a city where you have friends or family. For whatever reason, you can't expense your lodging on this trip (i.e., you don't have an expense account at your job, it's not a job-related trip, or the expense account won't cover this particular trip).

How long of a visit is too long to ask your friends/family if you can stay with them? Or, is it bad form to ask to stay at all (even for one night)? Does the rule vary depending on friend vs. family? Does the size of the dwelling of the friends/family make a difference? Is weekend vs. weekday relevant?

Let's limit "family" for the purpose of this discussion to siblings and aunts/uncles/cousins with whom you keep in touch on a regular basis. (I'm assuming it's a breach of etiquette to call up long-lost Great Aunt Beulah in San Diego to ask if you can bunk at her seaside condo for a week-long vacation.)

Summon your best Judith Martin impersonation and let me know your thoughts. If you can fashion a good rule of thumb, all the better. After some time for discussion in the comments, I'll update the post with my thoughts on the question.