It depends.
For my work computer, I screw them in tight, both on the monitor and the DP/VGA adapter.
For stationary devices (like overhead projectors) and extension cords, I screw them in, but not very tight.
For classroom computers, I only screw them in on the monitor and leave them unscrewed on the computer. Students can't keep their legs calm and often snag the cables. I prefer to let the connectors harmlessly disconnect instead of damaging the graphics card or motherboard.