Can you install a light switch without a ground?

Regarding this, how do you wire a light switch without ground?

If you are replacing a switch a ground is not required, as per the above exception. However, if you're installing a switch; replacement or otherwise, into a metal box that is grounded. The switch will be ground via the devices yoke and mounting screws. So if the metal box is grounded, the switch is also grounded.

Additionally, is a ground wire necessary? The appliance will operate normally without the ground wire because it is not a part of the conducting path which supplies electricity to the appliance. If the case is grounded, a high current should flow in the appliance ground wire and trip the breaker.

what can I use if I don't have a ground wire?

If the box is not grounded, you have two choices:

1. Run a ground to the box. This would mean running a new wire back to the panel (could be bare copper, but if you're doing the work may be better just to run a new wire - 14/3 would be the best), which could mean opening up drywall.
2. Wire the fan without ground.

Do all light switches have a ground wire?

If you are replacing a switch a ground is not required, as per the above exception. However, if you're installing a switch; replacement or otherwise, into a metal box that is grounded. The switch will be ground via the devices yoke and mounting screws. So if the metal box is grounded, the switch is also grounded.