Connect Arduino to Raspberry Pi with Tx/Rx

but we use 3 silicon diodes in series (5-3*0.6=3.2V) voltage drop or one 1.8 V Zener diode.

The problem with series diodes is you don't get any sinking current for a logic zero so you noise margin is shot.

Matous:
Grumpy_mike, would you please advise me what transistor would be suitable for this application? I need it to be fast enough to handle serial communication, but I'm not sure how to find it myself...

You would struggle to find a transistor that will not handle that speed, in electronic terms it is very slow. So any general purpose NPN transistor, the cheapest you can lay your hands on.

And if when using your circuit the Arduino RX pin is high for some reason, could it damage the transistor or even the Pi?

A rather bizarre set of circumstances there, not only has the RX ( normally set as an input ) got to be set as an output but it has to be set high as well. However, the output impedance of the aruino's output will limit the current to some extent and over current of the output is all that could happen.