Updated November 4, 2006
If your vehicle only squeeks when driving forwards or backwards and won't squeek when reving the engine in park the problem could be a dry or ready to blow u-joint. Check all of your u-joints for play or shiney metal around the caps. If you hear a quiet high pitched rotational sound apply your brake and see if it goes away. If it does this is just normal brake pad rubbing on the rotor.
What I do to check the drive line is the following.
On a flat surface I jack up one corner of the truck under the A-arm to get
the tire just off the ground.
I go under the truck and look at the halfshaft as it comes out of the geared
hub. I move the tire back and forth a bit and watch the half shaft. If I can
move the tire and the half shaft doesn't immediately move I know I have
freeplay in the geared hub.
Next do the same thing looking at the halfshaft as it comes out of the geared hub. Watch the brake rotor. When I rotate the tire back and forth and the input side of the halfshaft moves I see if the brake rotor is moving with the half shaft. If it isn't the halfshaft has freeplay. You might want to grab the rotor and move it while watching the half shaft at the hub.
Next I put a screw driver in the U joint on the input side of the diff and try to turn the diff. If the U joint is bad you will get freeplay/ wiggle in the joint. You can check all the U joints this way.
Then I chock the wheels that are still on the ground and put the tcase in Neutral. If you don't chock the wheels the truck will roll. I rotate the drive shaft watching for freeplay in the U joint as it enters the diff. As you turn the driveshaft watch the brake rotors for movement. If you can turn the driveshaft back and forth a bit and don't see movement in the output / rotors then you have freeplay in the diff. You can grab the rotor and driveshaft and move both to detect freeplay.
It's not unusual to have some freeplay. Only experience will tell you if there is too much. If you do all 4 corners you should find differences. If you find one diff much looser then the other then you may have a problem. If one halfshaft is tight and another has 1/4" of freeplay then you need a new halfshaft.
I've found that new half shafts don't have any discernable freeplay. Half shafts on high mileage trucks may have a little bit of movement. U joints shouldn't have any freeplay. Geared hubs have a little detectable freeplay. Diffs seem to be a big variable. In my opinion the tolerance of the diffs from the factory is pretty loose.