This is going to be popular string.
Moves in the military are not just moves, they are adventures.
The experience can be great or a total nightmare. Much of that depends on who does your moving.
My advice would be: if you don't have much in the way of possessions (single or small young family without much heavy furniture) or are not moving far, then do a DITY move (for the uninitiated, DITY stands for "Do IT Yourself"). I have been told that if you do it right, you can actually make money on DITY moves.
I, on the other hand, had moved enough times in my life prior to the Army and had enough crap to move that I swore I would never move myself again, so I have let the military move me. Since the Army contracts this out to private companies, the level of service can be incredibly variable. So far, I have been lucky, getting reliable and responsible moving companies. That's not always the case, and there seem to be countless horror stories about damage, lost items, stuff sent to the wrong place, etc.
For an Army run move, they will send out both movers and, if you want, packers (you can pack your own boxes or have professional packers). The packers show up a day or 2 before the move, and actually pack up everything in your house that is not nailed down (and I do mean EVERYTHING . . . they even packed a bag of garbage for us. Fortunately, there was nothing rottable in it). The packers we've had have been pretty good about fragile stuff. They've tended to actually "overpad" a lot of things (after all, they're billing uncle sam for all the materials, so they are probably "padding" their bills as well as your breakables.). Once everything is labeled, packed and tagged, the movers come and load up and move.
Depending on how long you have before you can actually get into your new home, your stuff may sit in a warehouse for a while. When you can actually move in, you contact the movers and they unload. Although I have never done it, you can actually get "Unpackers" too, or just unpack yourself.
If there is damage, missing stuff, etc, you can file a claim within a certain time frame (I think it's a year). The movers and packers should provide you with detailed lists of every box, piece of furniture, etc that was loaded and unloaded at both ends of the trip. It is your responsibility to check for damages and file any claims. So far, I've only had a couple minor dings on some large furniture and, surprisingly, no broken dishes, glassware, etc.
I'm sure the other active duty folks can add lots of comments.
