Quite a coincidence, as I'm currently reading a cozy mystery that includes this very question.
Here is my "hypothetical" answer, as (other than my children) I've never had anyone ask to live with me and my DH, except for a close friend who spent a short while here after Hurricane Katrina.
For people I am very close to -- parents, children, siblings, children of siblings, grandchildren -- my answer would be an unqualified yes, and the time limit would be highly negotiable (based mainly on not enabling someone to avoid making good choices). These are the people I will always be there for.
For not-family-but-close-friends -- it would depend on whether they were someone I could live with without going crazy. A definite time limit would have to be set. It also depends on whether it's one person, or a couple sharing a room, or a family with kids -- more than two people might well be more than we could handle.
For people who are not family or close friends, I'd probably refuse.
To me, the reason matters. I would be very sympathetic to "My company downsized, and I was laid off." But "I decided to quit working for awhile, so I could reflect on the wonders of nature" would leave me ice cold -- even from my children. Even from my much-adored grandchild.
Anyone staying with us would have to agree to some rules:
1) Rent/contribution to utilities/groceries, if they can reasonably afford it. If not, I'd let them stay for free.
2) Pitching in with housework/yardwork/cooking, and keeping common areas tidy.
3) If unemployed, the person must be actively looking for work (or attending school, if that was the agreement).
4) Rules about use of family room, TV, computers, house phone, tools, cars, washer/dryer, kitchen at meal times, personal possessions. (And the rule might be "no use at all.")
5) Rules about where they are allowed to keep their stuff. (Yes, your furniture is lovely, but I prefer my own, thankyouverymuch.)
6) Rules about guests, especially those who will be staying the night. (I'd be wary of having someone else who essentially moves in with the boarder, but without asking first.)
7) Any other rules needed to keep everyone sane and happy, such as "no loud noise after 10 pm" or "that's MY spot on the sofa" or "leave my Girl Scout Cookies alone if you like living."