The trick is to leave your stuff in bubblewrap. 
Amen! We’ve been here seven years and there are still unpacked boxes in the attic. I say, if we haven’t needed it seven years, heave ho! But, of course, it’s not MY stuff! I think there are several boxes of computer magazines with covers like “NEW! The 486!”
KSO’s master bedroom advice is most excellent. And one other thing that I think makes the bedroom move easier is spending the bucks (and not that much) on a wardrobe box with a hanging rod. Hang the stuff in it. Seal it up. Get it to the new place. Open it. Take the stuff out and hang it in the new closet. It beats the HELL out of taking everything off hangers. It even beats the hell out of a hanging rod in your car, because with that method you’re still schlepping handfuls of hangers – ow, ow, ow!
If you have books (and the time), put everything on an Excel spreadsheet & number the boxes & books. I’m selling off most of my 1300 books (email me for a list - lol) and this will prove invaluable, I think.
Don’t skimp on bubblewrap and/or clean newsprint.
Label EVERYTHING.
If U-Haul is involved, do not - and I repeat DO NOT - make your reservations through the internet or the 800 number. Call the local dealer & work directly with them. Trust me on this.
Be honest with yourself & then ruthless. If an item hasn’t been used in a year, do you really honestly need it? The more esoteric or outdated the item, the better the chance it can be tossed.
If you buy your supplies through a U-Haul dealer, they will buy back at full price the boxes you have not used/opened.
The heavier the items, the smaller the box they should be packed into.
Keep a separate box/area for things you’ll need to access right away - address book, check book, banking information, financial information, medical records, medications, etc.
If at all possible, don’t relocate your pets until you’re set up at the new place. It places less strain on them.
Good luck!
VCNJ~
Do not misunderestimate the time it’s going to take you to pack. If you’re packing at 2 AM before the move, you’re going to have boxes like “Toilet paper, 1 sock, Play-Doh, stuffed penguin, cheese”. You are going to hate those stupid boxes. Buckle down and really, really pack, because the “little bit I have left” is always much, much more than you think it is. I still have plenty of boxes like that in closets and such, and I know one of them has my lavender cardigan in it and I don’t know where it is.
Amen to this. I’ve self-moved (counting fingers) ten times in twenty years, and I still underestimate the number of boxes needed for books (too many) and how much time it takes to deal with all the weird crap I put aside for the end – papier-maché Mexican sculpture, the clothes hangers, that last floor lamp. You don’t want to run out of boxes or packing tape at midnight. Supermarkets don’t start parting with their discarded boxes until 6 AM, I’ve found.
My LPs have been in the same ugly milk crates for 2 decades and maybe 10,000 miles. It’s not an aesthetic decision – it’s just such a joy to be able to pick up the thing that they’re already in and take them down to the truck. One of these days Ikea will come up with bookshelves and dressers that just snap apart and you can carry them around with disturbing the books and the clothes and I will sign up for that in a heartbeat.
I like to use my kitchen towels for this purpose-- wrap each glass in a towel instead of newspaper. I’ve never had one break and it ensures that the towels are handy when you start unpacking.
Before you leave your old house, do a final walk-through. Every time I’ve moved, I’ve forgotten something. (If something’s been in the same place for years, you might not even notice it.) Look behind all the doors and in the nooks and crannies.
I recommend bringing lightbulbs along with the TP. Not every new house or apt still has lightbulbs screwed into the fixtures.
I’m going to second (or is it third?) the suggestion to wrap your dishes, glasses etc in paper towel. Saves a ton of time when you don’t have to wash everything before you put it away.
Also, make sure you have some table or floor lamps, since some rooms don’t have any built-in light fixtures and otherwise you’re going to be stumbling around in the dark.
And someone suggested boxes from the liquor store, which is a good idea. But at work today I thought of using the boxes that ten reams of copier paper comes in. They’re a convenient size and you might be able to get some for free from Kinkos or another copy center.
We have lots of junk, err, I mean stuff. Lots of it.
The last time we moved, I labeled boxes to go in specific rooms (ie, cloths, books, computers) but all of the misc stuff, that eventually you find the best place for but don’t use often, I stacked in the garage. I DIDN’T want to face a full stack of boxes full of less used stuff, while I was trying to figure out where the often used stuff would best go. Eventually, you look at what is left in that seldom used pile, and decide if it is really worth keeping.
Our friends still tease us. For a good 2 years, when asked where something was, the answer was oftern “In a 6ft radius in the garage”.