Open, there is not much space between the Corvette and the other car in the garage. Open makes it much easier to get in without hitting my head on the glass.
Eric

leave them open about an inch for ventiallation and car covered.
I like vetlover's idea about unlatching the t-tops but would be afraid of forgetting to re-latch them and driving off.
Hank

I've been told that the back window will wrinkle if the top is left down too much. I leave the windows up to keep the critters out.

When I'm gone it gets left however it was when my mom drove it last. When I'm home I continue the tradition. Keeps the wear and tear on the tops down not sliding them in and out.

Cat/Car stories.

My cat is a year and a month old now. Last summer I was working on the car, had the doors open for something and then closed them. Cat(Jester) jumped into the driver's footwell and was exploring as kittens of two or three months are often wont to do. Jester sees a bird flying past the back window and decides he is hungry. Launches onto the seat onto the center console and SMACK! RIGHT into the back window. I just about died laughing. He tried to play it off like nothing had happened.

My parents have a 01 Camry with a sunroof. My cat and my car live with my parents. Cat owns the place and likes sleeping on the warm hood of cars. However, when something piques his interest he's going to go investigate. He's walked across the roof of the Camry many times, and often walked across the glass sunroof while it was closed. Well, in keeping with tradition, mom parked the car and left the roof open, because, well, we'll be going out in four hours anyway. So Jester is walking across the car, fully expects the sunroof to be there and thinks nothing of the fact that he can see through the hole, he almost always can. Well, as you might imagine, today is different. Facefirst into the car. The myth that cats always land on their feet? Only when they expect to fall! I think it took him most of the fall to realize that he had been betrayed by the glass. Jester remains in perfect health and is becoming ever wiser to the deviousness of man.

Scot
Just had to share!