I never put a cigar out, at least not like a cigarette. I let it just go out naturally. Occasionally I'll have a waiter or bartender looking to clean out the ashtray and I'll tell them it's still lit. That's the last thing I need -- a garbage bin on fire from my cigar, LOL.
As far as when I let a smoke go out, I let the cigar and my taste buds tell me. I don't like cigars that get/burn very hot so I get sensitive to that. I also tend to draw more often so I am careful not to let the end get clogged, closed, etc. Overall, case by case basis.
Eric