Here are some alternatives for those occasions when you lack a screwdriver.
Tighten a steel washer into the chuck of a hand drill or brace and insert the edge into the screw slot. (This is also a good idea when you want to exert some extra leverage on a screw.) You can use a variable-speed power drill, too.
Check penknives around the house. Some may have a screwdriver blade.
A nail file can tighten a tiny screw - in spectacles, for example.
If you do have screwdrivers available, always choose one that fits the screw slot comfortably. Remember that the old Phillips screws have now been replaced by Supadriv screws, which have a more sophisticated slot design.
If you file a screwdriver tip, remember that the tip should be filed square, never to a point or wedge-shape. This ensures that the tip doesn't jump out of the slot when pressure is applied.
To increase the leverage when removing a difficult screw, clamp a self-grip wrench to the blade of the screwdriver, then use the wrench as a lever.
Invest in a set of jeweller's screw-drivers. They will prove invaluable for tiny screws.