Op-Amp Input Resistor?

IMO they serve no purpose, and they can be left out. If they were to minimize input offset, then there should also be one in the feedback from the output to the inverting input. Both inputs should see the same impedance.
Especially with very high input impedances like FET opamps there seems to be no need for them.

This may be a mistake in the circuit diagram. Possibly, the intent was that the 100K resistors be shunt resistors to the input, rather than in series. Shunt resistors would serve the purpose of lowering the input impedance to 100K. (Astronomical input impedance is not always desirable: for one thing, it is susceptible to noise.) The second purpose would be to provide a DC return if there is a coupling capacitor just before the input. Without the input referenced to ground, the capacitor will charge until it brings that input out of a useful range. Through a JFET input with a very tiny bias current, this could take hours or days!

Found a nice discussion of this here: http://www.analog.com/library/analogDialogue/archives/41-08/amplifier_circuits.html

(Nevertheless, this is "grasping at straws": because the circuit would then likely show the capacitor.)

As for having the resistors in series; I agree with the others. The likely reason would be current protection in case the input breaks down from overvoltage.

It is never discussed in the datasheet, but in practice, many voltage followers are unstable without the series input resistance. Try buiulding a voltage follower with an LME49710. Drive a 150 Ohm load. Use a 1 KHz sine wave. The output looks terrible, right? Now add a 10 KOhm series resistance on the input. Problem solved.

I too would like to hear an explanation for this.