Always zip mine up. I like to keep mine in the original shape. I bought a base shaper and organizer. When it's zipped, it looks brand new and no stretching or saggypants.
Zipped!!! i think it's silly to leave it unzipped as it will eventually distort the shape of the bag causing creasing and making it susceptible to cracking issues down the road.
I do a bit of both. I tend to leave her unzipped if I'm just nipping to the shops or if I'll be travelling by car so that I know I can easily reach my wallet. But tend to zip her up if I'm walking somewhere or if I'm travelling by tube or train and in a busy city.