While neon screwdrivers can give an indication of a live connection, lighting conditions and various combinations of wiring can result in the neon glow being invisible or absent. Floating high voltages will not necessarily light a neon bulb. A far safer alternative is a non contact voltage tester. These are available for a few pounds from most DIY and trade outlets. They run off a couple of AA or AAA batteries, so always check that the voltage tester works on a live part of the circuit before checking a suspect bit is truly powered down! Fitting a couple of Lithium batteries should ensure these devices work okay for up to ten years. Alkaline and zinc carbon batteries need frequent checking to make sure they are not leaking or have run flat.
In the absence of nothing better, a neon screwdriver can give an indication that a circuit is live, but are you comfortable betting your life on it? A suitably rated multimeter is my personal choice when checking for voltages.