I have an unusual problem that I'd like some input on. I have a '98 XJ with 125,000 miles and when I let it set for few minutes or longer and go to start it up it turns over without firing. The only way I can get it to start is by turning it over shortly THREE TIMES and finally on the third time it hits and starts up just like it should. NO hesitation. It started over a year ago and has gotten worse over time. Meaning It use to be the second try it would start up just fine. Now it takes three tries. Here is a list of things I've done to try and fix it.
Fuel pump, fuel filter, fuel pressure regulator, coil, wires, cap and rotor, coolant temp sensor, throttle body clean (including IAC), spark plugs.
Any suggestions or wild guesses will be appreciated. Thanx.

you could put a check vavle in your fuel line. maybe after you kill the engine all your fuel in the lines dump back into your tank, causing you to have to turn the key two or three times to get the fuel back to the spark plugs. JMO

I would look at the cps or cam pos sensor,on the cps you can disconnect it and check terminals b and c for resistance,it should read open,no resistance.

If you cycle the key a few times before trying to start will it fire the first time?

i agree .... sometimes if you cycle the key without actually starting it you will build up fuel pressure... it could be a weak pump ... i have a similar problem and as long as i turn the key and wait for the pump to finish priming itself before actually cranking the jeep it starts no problem ... also i would check your idle air control valve or (IAC VALVE) as some people call it ... if your valve is getting a little sticky it wont read what position the throttle is in an it will screw up the computer an it wont give the proper amount of fuel ... the iac valve is cheap too

Did you fix it? I would check the Neutral Safety Switch. I had that same problem and i pulled mine out and cleaned it and now she fires right up first try everytime.

I have the same problem. Did you come up with a solution??? It is an embarrassing problem. I just bought the Jeep last weekend and it's a problem I'd love to fix.

If it was the NSS switch, it wouldnt crank at all, let alone turn over/run.

CKP (aka CPS), would have a crank/no start senario. Mine does it periodically, when it does I just unplug and plug back in and it fires right up. So highly unlikely, but a small possibility. As for the CKP/testing it, there should be 100 ohms +/- 30, IIRC.
If it runs decent/well after start up, The Cam sensor is probably alright.

With my problem, yes it will fire the fire the first time if I cycle the key on and off three times. Does this mean fuel pump?

First, just try turning the key on and waiting three seconds before turning the key to crank position.

All XJs will start quicker (with fewer revolutions) if you allow the pump to pressurize the system first. It cuts cranking on mine in half, at least.

If this doesn't change things, you'll know where to look next.

Nope, same thing. It takes three fuel pump cycles to get it going. I assume "you'll know where to look next" means fuel pump!