While pressing the accelerator at speeds of 40-65 mph, my truck makes a "moaning" noise, kind of like a woman ghost (so hard to describe these sounds). I have a 4x4 2003 Quad Cab, and the noise comes from somehwere in the back half of my truck. It's about half as loud as a normal talking voice, and it's freakin obnoxious. I have definitely ruled out tires-on-pavement. Basically, I just want to know if anybody has experienced a similar kind of sound when they hit the gas at those speeds, or if this is just normal. This is not a sound that my truck has always made.

I would get your rear diff checked asap.
Could be your pinion gear.
Since its a 2003 go to your Dodge dealer and take the tech out for a spin
so you can duplicate the nosie.

Good luck

dude, my truck is in the shop for the ball joint recall right now. I had the same sound as you. kinda sounded like there is a turbo charger under the bed of my truck. I had them look at it. they just called me today. 800 to 1500 to fix it. it is the diff by the way. good luck.