For the truck it depends on anumber of things.
If the turbo & engine is cool, I usually shut down.
If I fuel at a truck stop which usually means hot & hot it stays running. Cannot hear me over the neighbors.

Winter, I always let it idle and usually run the Espar, too. If the temps are dropping and I cannot get Arctic diesel, I change the #2 to #1 ratio. Helps blend the fuel and keeps the Espar fuel line from gelling.

Living in cold country many people (understandably) leave their gasser idle while fueling in the winter and annoyingly do the same in the summer.

 

I turn on the high idle and let her run. Sometimes I shut it down only to drain water from the filter. Rather leave the runoff in thier parking lot than mine

 

Usually i shut mine off to avoid a runawy from gas fumes, During the winter if it's not warmed up yet i'll let her run wtih the doors locked.

 

I was told to shut her down so it doesn't blow a code for fuel cap being off. Anyone blow a code yet???

 

I thought the fuel cap code was a Ford thing. It happened to me when I had my Ranger. First time I filled up I must not have tightened the cap enough and I got a Check Engine light. I was ****** and went storming back to the dealer. They tightened my cap. I felt stupid. But really, why the fault code? They could have done something different to keep me sane. Another Ford thing is shutting off the fuel if you stop abruptly. I had to stop hard in traffic one day and it took me an hour to figure out why my truck stalled and wouldn't start. People were making fun of me, too, while I was pushing my truck off the road because it "stalled" I hated that POS. Too small. Too carlike, it felt like an econo box. I bought my first CTD, a 99, about a month later.

End rant.

I usually shut down when fueling. I don't want any hassle from attendants about a fire or anything. I leave it running if I just grabbing a beverage.