Safety must always remain priority number one when doing measurements with multimeters. Working safely, while making electrical measurements, is not rocket science. It’s a simple combination of careful planning, safe practices and using the right tools in the right way. The more voltage and current is present in the circuit, more careful you have to be. Fluke Safety video gives some overview on the multimeter measurements safety around power circuits.
Stock Multimeter Explosion shows one worst case scenario what can happen when you make mistakes with multimeter and high power energy source. This video illustrates why fused leads should be used with multi-meters. If you plug the leads in the wrong spot or have the wrong settings this is what happens. This video illustrates why fused leads should be used with multi-meters when measuring power circuits.
Check also High Energy Multimeter Destruction video for more examples of exploding multimeters and damages inside multimeters.