Is there a word in English which means non-meddlesome? What word is used to describe one who does not interfere in the affairs and business of others?

Hmmm, I can think of a bunch of almosts.
Reserved is more about preserving your own privacy. Uninterested, and distant have the aspect of don't care added.
Disinterested or detached both indicate impartiality rather than just the act of not interfering.

Anyone got anything better?
PS Welcome and good question.

sure: unintrusive, inofficious, hands-off, unengaged

-joe (laissez faire) friday

Yikes I knew it had been a hard day but I missed completely on all those.
Oh well, I'll stop AWADing and go home and make pickles.
Chow

PS I like unintrusive best, it has the same emotional tenor as non-meddlesome but sounds less awkward.

The word "laissez-faire" comes to mind. Kind of.

Yeah Hydra, it also came to Joe Friday's mind intermittently. (see above)

I just knew some folks didn't bother to read those intercalations.

-joe ('Mickey') friday

"Aloof" is the complete opposite, though it connotes anti-meddling, not neutrality.

I was interested in finding a word which does not express the thought in terms of a negative...i.e. not having un, dis, in, or non etc. as prefixes. Laissez-faire and hands off are close to what I want, but I thought perhaps there would be some eloquent sounding word which actually captures the virtue of not trying to influence the decisions of others...

enabling.
supportive.
parent.

Neutral?

It sounds like you want a word that connotes benevolence, though western culture (outside of Star Trek) tends to ennoble involvement.

I'd have thought that aloof was more along the lines of hard-hearted, haughty, incurious, and indifferent.

-joe (cold-fish) friday

Yah. "Removed"-- unwilling to get involved through haughtiness, etc. Neither benevolent nor neutral. Exactly.

Observer?

According to Plato, perhaps just "just."

I notice there are a few references to "Monroe Doctrinesque" on Googol.

Also, I don't see an adjectival form, but perhaps you could call someone a cincinnatus (after the roman dictator), but that reference might be too obscure and there is room for the reader to ascribe some other intention to the mention.