Tiny, you can check a u-joint by moving it to see if there is any unwanted movement like would happen if some of the needle bearings are toast. Another sure sign of a bad u-joint is rusty dust coming out of one of the bearing caps. When they go bad enough to cause a dramatic problem like 2004wranglerRHD's, it's not normally hard to find the bad u-joint if that is the problem.
2003WranglerRHD, I would unbolt the rear driveshaft and move the u-joints around to see if they feel secure & tight. Good u-joints will have no movement other than where they are supposed to rotate and then it should be somewhat stiff if the grease inside is in good condition.
They do go bad, that is for sure. A very good Spicer sealed (what I recommend) replacement u-joint is p/n 5-785x.