I'll let mine idle for at most 5 minutes once it's at operating temperature, other than that it gets shut down.
For me it has nothing to do with fuel efficiency or not wanting to pay for the fuel wasted idling. Any engine at idle (no load) has relatively cool cylinder temperatures that can't burn fuel properly, which leads to carbon buildup, sticking rings, etc.
Same thing with a wood fire in a stove, if it burns too cool you get creosote building up, with a hot fire all that's left is a fine ash.
One case where you DO want to have an idle cooldown period is on a turbocharged engine. If you've been working it hard, let it run at idle for 5-10 minutes before shutting down. This lets the turbo cool down gradually while fresh oil is still flowing through it, otherwise the heat left in the turbo will cook what oil is left in it.
Chilly