As has been already said it pretty much depends on the circumstances.
On the driveway if I'm going out again, yes I'll leave it down.
Popping into Tesco's for a pint of milk, Yes I'll leave it down.
If we are anywhere else or parking up for a few hours then its roof up.
I'm afraid ever since having had my garage broken into years ago and my Suzuki GZR1100K being taken out it (after a massive 6 weeks of ownership)and being told by the police Officer who attended about a classic car that had been stolen, where they had broken into the family car parked against the garage door which they moved out of the way to gain access. I've been of the opinion that if some low life scum want's what you have there's not a lot you can do about it the only thing you can do is try and stop the opportunist. So in the same way they tell you to leave nothing on display in a 'normal car' I always make sure nothing is on display roof up or down.