ESD Protection for UART and I2C

To address a possible confusion that hasn't been mentioned in answers so far:

A resistor between ESD source and TVS, doesn't do much. Indeed a small chip resistor is likely to spark over, or even blow up entirely. So that's out.

But that's not to say resistors are worthless here. Simply transposing the resistor and TVS does provide value, quite a lot in fact.

Also, don't use bidirectional TVS. Use clamp diodes, preferably array types. This reflects the clamping voltage of the ICs, which are almost always to their supply pins (the datasheet will say -0.3V/VDD+0.3V voltage range, or something like that, for such pins).

I won't go into deep explanation here, but you may find this reading list helpful:

Simple model into RC filter, demonstrating clamp diodes, and series resistor (after TVS) efficacy:
Is a 100 Ω/1 nF RC low-pass filter enough to protect a microcontroller I/O pin from ESD?

Discussion of standards and ratings, and the effect of TVS and resistors:
How much current can opamps' integrated ESD diodes carry during an ESD strike?

ESD example including a system diagram, relevant to board/system layout:
More robust MOSFET gate: Which parameter to watch?

Finally, don't use I2C off-board. It's literally intended for on-board application only. I2C over screw terminals is absolutely the wrong way to use it. Further reading:
Can I use I2C over 2m cables?

There are proper ways to send I2C farther, but it's a force-fit, often expensive (e.g. some LT parts), and you should really just reconsider the application in general.

The same advice applies to logic-level UART signals. Perhaps the connection is short range and low baud rate, and some filtering and ESD protection will suffice. Preferably, it's converted to RS-232 or -422 levels, and sent over modest to large distances with good signal quality.

My question is: is it necessary to add a resistor for ESD protection?

Generally for ESD, the discharge is thousands of volts sourced from an impedance of hundreds of ohms hence, into a TVS there is a current pulse of several tens of amps. Pretty much most TVS diodes can survive this but, always check the data sheets as to what they say. In addition, the resulting current pulse from an ESD discharge expends its energy in a lot less than 1 μs: -

Read more at: Electrostatic Discharge Test for Energy Meters.

So, you will see a peak current of tens of amps and, pretty much, all the energy is gone in less than 100 ns. But this also depends on what ESD specification you are designing to make your equipment resilient against hence, it's a numbers gain and the above graph is level 4 EN61000-4-2.

Nevertheless, in the main case, most TVS diodes will clamp to some smallish voltage (tens of volts) whilst conducting the tens of amps current from an ESD surge. Adding a series resistor before the TVS is just asking for trouble because then you need to ensure that the resistor will take its share of the energy surge. So, it's inadvisable to do this.

In short, choose a TVS that clamps as low as possible without causing normal operation to be compromised. Then, you should consider how much resilience your "victim" circuit has to the tens of volts that the TVS clamps to. You might find that your victim circuit is no longer a potential victim and can handle the TVS suppressed surge but, if not, you may decide to add a series resistor between TVS and the victim in order to limit current to a few mA.

What is your opinion on which way is best and any other commonly practiced methods for this?

Use a TVS or, use an isolating interface but, the use of a TVS is much more common.