Without screen: absolutely not! I'd be terrified!
With screen: I guess it depends on the cat, but Minion is not at all the type to try to rip up the screen to get out, so almost all summer I have windows open so he can sit on the ledge and check out the outdoors. The only time I close the windows during the summer months are the days that are so hot that we need to crank on the A.C..

I don't blame you for being fearful of kitties in open, screenless windows. I'd not like to see that either.