Burning Arduinos one after another
Measurements to prevent breaking an Arduino (or AVR in general):

Precautions


Always remove the USB or adapter plug when you make a change in the circuit.
Check all wires before you switch it on.
Remove or make sure (temporary) loose wires/jumpers do not touch other components or the Arduino (better take them out or 'park' them somewhere else in the breadboard.


Preventing wanted changes resulting in shortcuts


Check again the wires/jumpers you just changed/added.
Make sure no other components/wires/jumpers are touching the Arduino or the breadboard (components).
Clean your desk (if you have space), so if something metal falls/moves, it does not hurt your Arduino.
When changing a shield, always check all wiring to and from it, to your Arduino and the components on the shield itself if needed.


Preventing component shortcuts or overpowering


If you have a wire from a pin to GND or a pin to VSS, always make sure there is either a resistor, or you know why a resistor is not needed. This can also damage directly your Arduino.
Make sure that every component does not get more power than it can handle.
More specific: If you have components using 3.3V, make sure they don't get 5V.
If you have components using 3.3V, make sure they don't get 5V.


Preventing too much heat


Do not just put an Arduino in some case/enclosure ... heat may destroy it, so check before there is enough cooling, add a fan, heatsink or make holes in the enclosure.
If you connect any power source other than USB, check again if it does not generate unnecessary much heat. Unused voltage will generate much heat.


Preventing static electricity


Do not touch components when not needed
If you touch components, make sure you are discharged (touch a radiator, use a wrist band, use an ESD mat, touch grounded wire).


Preventing trivial mistakes


Do not keep drinks next to your Arduino or breadboard (or if you, keep it on the other side).
Watch out for heavy cables not dragging your Arduino from the table/desk ... a USB cable can easily drag an Arduino down.
Watch out when you change cables, not to pull your Arduino from the table/desk.
Keep animals (and people too, to your own judgement) away from your electronics project.