Resistors in series with Tx and Rx

One of them is there to prevent damage that could occur if the AVR has RxD programmed as an output, pins on both devices could be damaged if that happened as AVR pins can source and sink quite a lot of current. I don't think that the other resistor is necessary.

It doesn't look like there is any good reason for those resistors. Both parts on that schematic appear to run on 5V with a common ground. There should be no need for resistors in the lines between the two chips.

If the lines were going off board, then there might be some point to putting resistors in series to protect the on-board parts, but that doesn't seem to be what's happening in that schematic.

Keep in mind this is a Arduino schematic. That means there is a good chance whoever designed it doesn't do this professionally. There are a lot of superstitions out there. Just because something is on the net doesn't mean it's done right.

This is an old and already answered question, but I didn't find in any of the answers one of the good and possibly one of the most important reasons for the resistors to be there.

Although most people use the RX/TX only to connect the Arduino to their PCs for programming the chip and/or perform serial debugging, others use the Arduino's RX/TX pins to communicate it with other serial devices. In this case, the FTDI chip and this other device would conflict and it is very likely that will damage both due to short circuiting. These resistors "separate" the FTDI from the other device when there is one connected to the AVR RX/TX pins, protecting both and allowing them to be wired and connected simultaneously.

One thing to remember is that, once another serial device is connected to the RX/TX pins of Arduino, the resistors will mask the logical levels from the FTDI in a similar way that happens with pullup/pulldown resistors, so, the external device will have "preference" over the FTDI communication.