Do you like your speakers fully clothed or naked?
I keep them fully clothed. They get self-conscious.
Do you use your home theater speakers with the grills on or off? Why?
To be serious, I keep them on mostly because they look incomplete without, due the rubber grommet mounting plugs in my M&Ks. It also offers some form of protection, since people can walk up to them. If I had an acoustically transparent screen I'd probably take them off and then backlight behind the screen so I could flip a light on and show them off.
My studio monitors I keep the grills on even, but they are super-thin and you can see the drivers through the cloth. My speakers at work don't have grills or mounting bungs for them.
What would make you switch to the opposite?
I think speakers can look very cool without grills if they are designed to be run that way, hiding how they mount. On front dual slot ported speakers this could be done with recessed clips on either side. Otherwise a magnetic mounting setup could be used, with small magnets mounted on the inside face of the speaker, and then the opposite polarity piece mounted on the grill. That way they would just 'clamp' on but you wouldn't see the mounting method if you used them without. I also think this would be cheaper for manufacturers than having to cut the four holes and buy rubber grommets.