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.

I thought it has protection against that.

Genuine Arduinos do have some protection, yes.

Is it normal for them to react like that so easily?

Cheap rubbish? Sure. You get what you pay for.

How can I prevent this happening AGAIN..

Buy a real one. Also be more careful.

But at the price you pay for cheap clones, do you really care if they end up broken? You can buy many clones for each genuine one, and while a genuine one may last longer, when you do manage to kill it (they aren't that much more rugged, but some components are more reliable, such as the USB interface chip), which you seem adept at, you would be far more upset than if you'd killed a clone.

So I would suggest invest in one Genuine one for special projects, and to support Arduino (if no one buys Genuine boards there will be no Arduino), and a pile of clones that you can experiment and learn with. Blow them up at will, and when you are happy with your project transfer it over to the genuine board for showing off to people.

Always use a series resistor when connecting anything to your IO pins. In many cases you will need one anyway (like driving a LED or a BJT), and in other cases it will not hurt (like driving MOSFET gates or UART lines). A 100 Ohm resistor will limit the current to 50 mA (keeping it within the safe range), while having little effect on your circuit in most cases.